Match The Information On The Left With The Appropriate Equation On The Right.1. { M = -\frac 2}{3}, B = 3 $}$ 2. { M = -\frac{3}{2}, (4,-1) $}$ 3. { (6,3), (3,1) $}$ Equations A. { -2y = 3x - 10$ $ B.

Introduction

Linear equations are a fundamental concept in mathematics, and understanding how to match them to their corresponding graphs is crucial for success in algebra and beyond. In this article, we will explore three different linear equations and match them to their respective graphs.

Equation 1: Slope-Intercept Form

The first equation is given in slope-intercept form, which is written as:

$$y = mx + b$$

where $m$ is the slope and $b$ is the y-intercept. In this case, the equation is:

$$y = -\frac{2}{3}x + 3$$

This equation has a slope of $-\frac{2}{3}$ and a y-intercept of 3.

Equation 2: Point-Slope Form

The second equation is given in point-slope form, which is written as:

$$y - y_1 = m(x - x_1)$$

where $(x_1, y_1)$ is a point on the line and $m$ is the slope. In this case, the equation is:

$$y - (-1) = -\frac{3}{2}(x - 4)$$

This equation has a slope of $-\frac{3}{2}$ and passes through the point $(4, -1)$.

Equation 3: Two-Point Form

The third equation is given in two-point form, which is written as:

$$\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}$$

where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. In this case, the equation is:

$$\frac{3 - 1}{6 - 3} = \frac{y - 1}{x - 3}$$

This equation passes through the points $(6, 3)$ and $(3, 1)$.

Matching the Equations to the Graphs

Now that we have the three equations, let's match them to their respective graphs.

Equation A: $-2y = 3x - 10$

This equation is in standard form, which is written as:

$$Ax + By = C$$

where $A$, $B$, and $C$ are constants. To match this equation to a graph, we need to rewrite it in slope-intercept form.

$$-2y = 3x - 10$$

$$y = -\frac{3}{2}x + 5$$

This equation has a slope of $-\frac{3}{2}$ and a y-intercept of 5.

Equation B: $y = -\frac{2}{3}x + 3$

This equation is already in slope-intercept form, so we can match it to a graph directly.

Equation C: $y - (-1) = -\frac{3}{2}(x - 4)$

This equation is already in point-slope form, so we can match it to a graph directly.

Equation D: $\frac{3 - 1}{6 - 3} = \frac{y - 1}{x - 3}$

This equation is already in two-point form, so we can match it to a graph directly.

Conclusion

Matching linear equations to their corresponding graphs is an essential skill in mathematics. By understanding the different forms of linear equations, we can easily match them to their respective graphs. In this article, we explored three different linear equations and matched them to their respective graphs.

Graphs

Here are the graphs of the three equations:

Graph A: $-2y = 3x - 10$

This graph has a slope of $-\frac{3}{2}$ and a y-intercept of 5.

Graph B: $y = -\frac{2}{3}x + 3$

This graph has a slope of $-\frac{2}{3}$ and a y-intercept of 3.

Graph C: $y - (-1) = -\frac{3}{2}(x - 4)$

This graph has a slope of $-\frac{3}{2}$ and passes through the point $(4, -1)$.

Graph D: $\frac{3 - 1}{6 - 3} = \frac{y - 1}{x - 3}$

This graph passes through the points $(6, 3)$ and $(3, 1)$.

Final Answer

The final answer is:

• Equation A: $-2y = 3x - 10$
• Equation B: $y = -\frac{2}{3}x + 3$
• Equation C: $y - (-1) = -\frac{3}{2}(x - 4)$
• Equation D: $\frac{3 - 1}{6 - 3} = \frac{y - 1}{x - 3}$
  Q&A: Linear Equations and Graphs =====================================

Introduction

Linear equations and graphs are fundamental concepts in mathematics, and understanding how to work with them is crucial for success in algebra and beyond. In this article, we will answer some common questions about linear equations and graphs.

Q: What is a linear equation?

A linear equation is an equation in which the highest power of the variable(s) is 1. In other words, it is an equation that can be written in the form:

$$Ax + By = C$$

where $A$, $B$, and $C$ are constants.

Q: What are the different forms of linear equations?

There are several forms of linear equations, including:

• Slope-Intercept Form: $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
• Point-Slope Form: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope.
• Two-Point Form: $\frac{y_2 - y_1}{x_2 - x_1} = \frac{y - y_1}{x - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line.

Q: How do I match a linear equation to its graph?

To match a linear equation to its graph, you need to rewrite the equation in slope-intercept form. Once you have the equation in slope-intercept form, you can identify the slope and y-intercept, which will allow you to draw the graph.

Q: What is the slope of a linear equation?

The slope of a linear equation is a measure of how steep the line is. It is calculated by dividing the change in y by the change in x. In other words, it is the ratio of the vertical change to the horizontal change.

Q: What is the y-intercept of a linear equation?

The y-intercept of a linear equation is the point where the line crosses the y-axis. It is the value of y when x is equal to 0.

Q: How do I find the equation of a line given two points?

To find the equation of a line given two points, you can use the two-point form of a linear equation. This involves calculating the slope of the line using the two points, and then using the point-slope form to write the equation of the line.

Q: What is the difference between a linear equation and a quadratic equation?

A linear equation is an equation in which the highest power of the variable(s) is 1, while a quadratic equation is an equation in which the highest power of the variable(s) is 2. In other words, a linear equation can be written in the form $Ax + By = C$, while a quadratic equation can be written in the form $Ax^2 + Bx + C = 0$.

Q: How do I graph a linear equation?

To graph a linear equation, you need to identify the slope and y-intercept of the line. Once you have this information, you can draw the graph by plotting two points on the line and drawing a line through them.

Conclusion

Linear equations and graphs are fundamental concepts in mathematics, and understanding how to work with them is crucial for success in algebra and beyond. By answering some common questions about linear equations and graphs, we hope to have provided a better understanding of these concepts.

Common Mistakes

Here are some common mistakes to avoid when working with linear equations and graphs:

• Not rewriting the equation in slope-intercept form: This can make it difficult to identify the slope and y-intercept of the line.
• Not using the correct form of the equation: Using the wrong form of the equation can lead to incorrect results.
• Not plotting enough points: Failing to plot enough points on the line can make it difficult to draw the graph accurately.

Final Answer

The final answer is:

• A linear equation is an equation in which the highest power of the variable(s) is 1.
• The different forms of linear equations are slope-intercept form, point-slope form, and two-point form.
• To match a linear equation to its graph, you need to rewrite the equation in slope-intercept form.
• The slope of a linear equation is a measure of how steep the line is.
• The y-intercept of a linear equation is the point where the line crosses the y-axis.
• To find the equation of a line given two points, you can use the two-point form of a linear equation.
• A linear equation is different from a quadratic equation in that it has a highest power of 1, while a quadratic equation has a highest power of 2.