Which Is The Graph Of The Equation Y − 1 = 2 3 ( X − 3 Y - 1 = \frac{2}{3}(x - 3 Y − 1 = 3 2 ​ ( X − 3 ]?

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Understanding the Equation

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The given equation is in the form of a linear equation, which is a polynomial equation of degree one. It is represented as $y - 1 = \frac{2}{3}(x - 3)$. This equation can be graphed on a coordinate plane to visualize the relationship between the variables x and y.

Graphing Linear Equations

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To graph a linear equation, we need to find the slope and the y-intercept. The slope of the equation is the coefficient of x, which is $\frac{2}{3}$. The y-intercept is the value of y when x is equal to zero. In this case, the y-intercept is 1.

Finding the Slope

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The slope of the equation is $\frac{2}{3}$. This means that for every one unit increase in x, y increases by $\frac{2}{3}$ units. This is a positive slope, indicating that the line slopes upward from left to right.

Finding the Y-Intercept

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The y-intercept of the equation is 1. This means that when x is equal to zero, y is equal to 1. This is the point where the line intersects the y-axis.

Graphing the Line

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To graph the line, we can use the slope and the y-intercept to find two points on the line. We can then draw a line through these two points to represent the equation.

Finding Two Points on the Line

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To find two points on the line, we can substitute different values of x into the equation and solve for y. Let's substitute x = 0 and x = 3 into the equation.

Substituting x = 0

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When x is equal to zero, the equation becomes:

$y - 1 = \frac{2}{3}(0 - 3)$

Simplifying the equation, we get:

$y - 1 = -2$

Adding 1 to both sides, we get:

$y = -1$

So, when x is equal to zero, y is equal to -1. This is the first point on the line.

Substituting x = 3

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When x is equal to 3, the equation becomes:

$y - 1 = \frac{2}{3}(3 - 3)$

Simplifying the equation, we get:

$y - 1 = 0$

Adding 1 to both sides, we get:

$y = 1$

So, when x is equal to 3, y is equal to 1. This is the second point on the line.

Drawing the Line

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Now that we have two points on the line, we can draw a line through these two points to represent the equation. The line will have a slope of $\frac{2}{3}$ and a y-intercept of 1.

Conclusion

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In conclusion, the graph of the equation $y - 1 = \frac{2}{3}(x - 3)$ is a line with a slope of $\frac{2}{3}$ and a y-intercept of 1. The line passes through the points (0, -1) and (3, 1).

Visualizing the Graph

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Here is a visual representation of the graph:

  +---------------+
  |              |
  |  (0, -1)    |
  |              |
  +---------------+
  |              |
  |  (3, 1)     |
  |              |
  +---------------+
  |              |
  |  y = 1      |
  |              |
  +---------------+
  |              |
  |  x = 3     |
  |              |
  +---------------+

Graphing Linear Equations in Slope-Intercept Form

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The equation $y - 1 = \frac{2}{3}(x - 3)$ can also be written in slope-intercept form as $y = \frac{2}{3}x + 1$. This form makes it easier to identify the slope and the y-intercept.

Conclusion

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In conclusion, the graph of the equation $y - 1 = \frac{2}{3}(x - 3)$ is a line with a slope of $\frac{2}{3}$ and a y-intercept of 1. The line passes through the points (0, -1) and (3, 1). The equation can also be written in slope-intercept form as $y = \frac{2}{3}x + 1$.

Graphing Linear Equations in Standard Form

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The equation $y - 1 = \frac{2}{3}(x - 3)$ can also be written in standard form as $y = \frac{2}{3}x - 2 + 1$. This form makes it easier to identify the slope and the y-intercept.

Conclusion

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In conclusion, the graph of the equation $y - 1 = \frac{2}{3}(x - 3)$ is a line with a slope of $\frac{2}{3}$ and a y-intercept of 1. The line passes through the points (0, -1) and (3, 1). The equation can also be written in slope-intercept form as $y = \frac{2}{3}x + 1$ and in standard form as $y = \frac{2}{3}x - 1$.

Graphing Linear Equations in Point-Slope Form

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The equation $y - 1 = \frac{2}{3}(x - 3)$ can also be written in point-slope form as $y - 1 = \frac{2}{3}(x - 3)$. This form makes it easier to identify the slope and the y-intercept.

Conclusion

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In conclusion, the graph of the equation $y - 1 = \frac{2}{3}(x - 3)$ is a line with a slope of $\frac{2}{3}$ and a y-intercept of 1. The line passes through the points (0, -1) and (3, 1). The equation can also be written in slope-intercept form as $y = \frac{2}{3}x + 1$, in standard form as $y = \frac{2}{3}x - 1$, and in point-slope form as $y - 1 = \frac{2}{3}(x - 3)$.

Graphing Linear Equations in General Form

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The equation $y - 1 = \frac{2}{3}(x - 3)$ can also be written in general form as $y - 1 = \frac{2}{3}x - 2 + 1$. This form makes it easier to identify the slope and the y-intercept.

Conclusion

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In conclusion, the graph of the equation $y - 1 = \frac{2}{3}(x - 3)$ is a line with a slope of $\frac{2}{3}$ and a y-intercept of 1. The line passes through the points (0, -1) and (3, 1). The equation can also be written in slope-intercept form as $y = \frac{2}{3}x + 1$, in standard form as $y = \frac{2}{3}x - 1$, in point-slope form as $y - 1 = \frac{2}{3}(x - 3)$, and in general form as $y - 1 = \frac{2}{3}x - 1$.

Graphing Linear Equations in Parametric Form

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The equation $y - 1 = \frac{2}{3}(x - 3)$ can also be written in parametric form as $x = t + 3$ and $y = \frac{2}{3}t + 1$. This form makes it easier to identify the slope and the y-intercept.

Conclusion

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In conclusion, the graph of the equation $y - 1 = \frac{2}{3}(x - 3)$ is a line with a slope of $\frac{2}{3}$ and a y-intercept of 1. The line passes through the points (0, -1) and (3, 1). The equation can also be written in slope-intercept form as $y = \frac{2}{3}x + 1$, in standard form as $y = \frac{2}{3}x - 1$, in point-slope form as $y - 1 = \frac{2}{3}(x - 3)$, in general form as $y - 1 = \frac{2}{3}x - 1$, and in parametric form as $x = t + 3$ and $y = \frac{2}{3}t + 1$.

Graphing Linear Equations in Polar Form

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The equation $y - 1 = \frac{2}{3}(x - 3)$ can also be written in polar form as $r = \frac{2}{3}\theta + 1$. This form makes it easier to identify the slope and the y-intercept.

Conclusion

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In conclusion, the graph of the equation $y - 1 = \frac{2}{3}(x - 3

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Q: What is the graph of the equation $y - 1 = \frac{2}{3}(x - 3)$?

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A: The graph of the equation $y - 1 = \frac{2}{3}(x - 3)$ is a line with a slope of $\frac{2}{3}$ and a y-intercept of 1. The line passes through the points (0, -1) and (3, 1).

Q: How do I graph a linear equation?

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A: To graph a linear equation, you need to find the slope and the y-intercept. The slope is the coefficient of x, and the y-intercept is the value of y when x is equal to zero. You can then use these values to find two points on the line and draw a line through them.

Q: What is the slope of the equation $y - 1 = \frac{2}{3}(x - 3)$?

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A: The slope of the equation $y - 1 = \frac{2}{3}(x - 3)$ is $\frac{2}{3}$. This means that for every one unit increase in x, y increases by $\frac{2}{3}$ units.

Q: What is the y-intercept of the equation $y - 1 = \frac{2}{3}(x - 3)$?

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A: The y-intercept of the equation $y - 1 = \frac{2}{3}(x - 3)$ is 1. This means that when x is equal to zero, y is equal to 1.

Q: How do I find the slope and y-intercept of a linear equation?

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A: To find the slope and y-intercept of a linear equation, you need to rewrite the equation in slope-intercept form, which is $y = mx + b$, where m is the slope and b is the y-intercept.

Q: What is the slope-intercept form of the equation $y - 1 = \frac{2}{3}(x - 3)$?

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A: The slope-intercept form of the equation $y - 1 = \frac{2}{3}(x - 3)$ is $y = \frac{2}{3}x + 1$.

Q: What is the standard form of the equation $y - 1 = \frac{2}{3}(x - 3)$?

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A: The standard form of the equation $y - 1 = \frac{2}{3}(x - 3)$ is $y = \frac{2}{3}x - 2 + 1$, which simplifies to $y = \frac{2}{3}x - 1$.

Q: What is the point-slope form of the equation $y - 1 = \frac{2}{3}(x - 3)$?

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A: The point-slope form of the equation $y - 1 = \frac{2}{3}(x - 3)$ is $y - 1 = \frac{2}{3}(x - 3)$.

Q: What is the general form of the equation $y - 1 = \frac{2}{3}(x - 3)$?

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A: The general form of the equation $y - 1 = \frac{2}{3}(x - 3)$ is $y - 1 = \frac{2}{3}x - 2 + 1$, which simplifies to $y - 1 = \frac{2}{3}x - 1$.

Q: What is the parametric form of the equation $y - 1 = \frac{2}{3}(x - 3)$?

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A: The parametric form of the equation $y - 1 = \frac{2}{3}(x - 3)$ is $x = t + 3$ and $y = \frac{2}{3}t + 1$.

Q: What is the polar form of the equation $y - 1 = \frac{2}{3}(x - 3)$?

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A: The polar form of the equation $y - 1 = \frac{2}{3}(x - 3)$ is $r = \frac{2}{3}\theta + 1$.

Q: How do I graph a linear equation in different forms?

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A: To graph a linear equation in different forms, you need to rewrite the equation in the desired form and then use the slope and y-intercept to find two points on the line and draw a line through them.

Q: What are the different forms of a linear equation?

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A: The different forms of a linear equation are:

• Slope-intercept form: $y = mx + b$
• Standard form: $Ax + By = C$
• Point-slope form: $y - y_1 = m(x - x_1)$
• General form: $Ax + By + C = 0$
• Parametric form: $x = t + a$ and $y = mt + b$
• Polar form: $r = m\theta + b$

Q: How do I choose the best form for graphing a linear equation?

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A: The best form for graphing a linear equation depends on the specific equation and the information you need to graph. You may need to rewrite the equation in different forms to find the one that is most convenient for graphing.

Q: What are some common mistakes to avoid when graphing linear equations?

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A: Some common mistakes to avoid when graphing linear equations include:

• Not rewriting the equation in the desired form
• Not finding the slope and y-intercept
• Not using the correct values for the slope and y-intercept
• Not drawing a line through the correct points
• Not labeling the axes and title of the graph

Q: How do I check my work when graphing linear equations?

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A: To check your work when graphing linear equations, you can:

• Verify that the slope and y-intercept are correct
• Check that the line passes through the correct points
• Make sure that the line is drawn correctly
• Label the axes and title of the graph correctly

Q: What are some real-world applications of graphing linear equations?

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A: Some real-world applications of graphing linear equations include:

• Modeling population growth
• Calculating the cost of goods
• Determining the area of a rectangle
• Finding the distance between two points
• Graphing the relationship between two variables

Q: How do I use graphing linear equations in real-world applications?

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A: To use graphing linear equations in real-world applications, you can:

• Identify the variables and constants in the equation
• Rewrite the equation in the desired form
• Use the slope and y-intercept to find the solution
• Graph the equation to visualize the relationship between the variables
• Use the graph to make predictions or decisions.