A. Rewrite The Given Equation 5 X + 6 Y − 30 = 0 5x + 6y - 30 = 0 5 X + 6 Y − 30 = 0 In Slope-intercept Form.b. Give The Slope And Y Y Y -intercept.c. Use The Slope And Y Y Y -intercept To Graph The Linear Function.- A. The Slope-intercept Form Of The Equation Is

a. Rewrite the given equation $5x + 6y - 30 = 0$ in slope-intercept form.

The slope-intercept form of a linear equation is given by the formula $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept. To rewrite the given equation in slope-intercept form, we need to isolate the variable $y$ on one side of the equation.

First, let's add 30 to both sides of the equation to get rid of the constant term on the left-hand side:

$$5x + 6y = 30$$

Next, we'll subtract $5x$ from both sides to isolate the term with $y$:

$$6y = -5x + 30$$

Now, we'll divide both sides by 6 to solve for $y$:

$$y = \frac{-5}{6}x + 5$$

Therefore, the slope-intercept form of the given equation is $y = \frac{-5}{6}x + 5$.

b. Give the slope and $y$-intercept.

The slope-intercept form of the equation is $y = \frac{-5}{6}x + 5$. From this equation, we can see that the slope is $\frac{-5}{6}$ and the $y$-intercept is 5.

c. Use the slope and $y$-intercept to graph the linear function.

To graph the linear function, we can use the slope and $y$-intercept. The slope tells us the direction and steepness of the line, while the $y$-intercept tells us where the line intersects the $y$-axis.

Since the slope is $\frac{-5}{6}$, which is negative, the line will slope downward from left to right. The $y$-intercept is 5, which means that the line will intersect the $y$-axis at the point (0, 5).

To graph the line, we can start at the $y$-intercept and use the slope to find another point on the line. For example, we can move 1 unit to the right and 5/6 units down to find another point on the line. We can continue this process to find more points on the line and draw a smooth curve through them.

Here's a step-by-step guide to graphing the linear function:

1. Start at the $y$-intercept (0, 5).
2. Move 1 unit to the right and 5/6 units down to find another point on the line.
3. Continue this process to find more points on the line.
4. Draw a smooth curve through the points to graph the linear function.

By following these steps, we can graph the linear function and visualize the relationship between the variables $x$ and $y$.

Example Use Case

Suppose we want to find the value of $y$ when $x = 2$. We can plug $x = 2$ into the equation $y = \frac{-5}{6}x + 5$ to get:

$$y = \frac{-5}{6}(2) + 5$$

Simplifying the equation, we get:

$$y = \frac{-10}{6} + 5$$

$$y = \frac{-10 + 30}{6}$$

$$y = \frac{20}{6}$$

$$y = \frac{10}{3}$$

Therefore, when $x = 2$, the value of $y$ is $\frac{10}{3}$.

Conclusion

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

A: The slope-intercept form of a linear equation is given by the formula $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

Q: How do I rewrite a linear equation in slope-intercept form?

A: To rewrite a linear equation in slope-intercept form, you need to isolate the variable $y$ on one side of the equation. You can do this by adding or subtracting the same value to both sides of the equation, and then dividing both sides by the coefficient of $y$.

Q: What is the slope of the line in the equation $y = \frac{-5}{6}x + 5$?

A: The slope of the line in the equation $y = \frac{-5}{6}x + 5$ is $\frac{-5}{6}$.

Q: What is the $y$-intercept of the line in the equation $y = \frac{-5}{6}x + 5$?

A: The $y$-intercept of the line in the equation $y = \frac{-5}{6}x + 5$ is 5.

Q: How do I graph a linear function using the slope and $y$-intercept?

A: To graph a linear function using the slope and $y$-intercept, you can start at the $y$-intercept and use the slope to find another point on the line. You can continue this process to find more points on the line and draw a smooth curve through them.

Q: What is the value of $y$ when $x = 2$ in the equation $y = \frac{-5}{6}x + 5$?

A: To find the value of $y$ when $x = 2$ in the equation $y = \frac{-5}{6}x + 5$, you can plug $x = 2$ into the equation and solve for $y$. The value of $y$ is $\frac{10}{3}$.

Q: Can I use the slope-intercept form to find the value of $x$ when $y$ is given?

A: Yes, you can use the slope-intercept form to find the value of $x$ when $y$ is given. You can plug the value of $y$ into the equation and solve for $x$.

Q: What are some real-world applications of the slope-intercept form?

A: The slope-intercept form has many real-world applications, such as modeling the relationship between two variables, finding the equation of a line, and graphing linear functions. It is also used in physics, engineering, and economics to model real-world phenomena.

Q: Can I use the slope-intercept form to find the equation of a line that is not in slope-intercept form?

A: Yes, you can use the slope-intercept form to find the equation of a line that is not in slope-intercept form. You can rewrite the equation in slope-intercept form by isolating the variable $y$ on one side of the equation.

Q: What are some common mistakes to avoid when rewriting a linear equation in slope-intercept form?

A: Some common mistakes to avoid when rewriting a linear equation in slope-intercept form include:

• Not isolating the variable $y$ on one side of the equation
• Not dividing both sides of the equation by the coefficient of $y$
• Not checking for extraneous solutions

Q: Can I use a calculator to find the slope and $y$-intercept of a line?

A: Yes, you can use a calculator to find the slope and $y$-intercept of a line. You can enter the equation of the line into the calculator and use the built-in functions to find the slope and $y$-intercept.

Q: What are some tips for graphing a linear function using the slope and $y$-intercept?

A: Some tips for graphing a linear function using the slope and $y$-intercept include:

• Start at the $y$-intercept and use the slope to find another point on the line
• Continue this process to find more points on the line
• Draw a smooth curve through the points to graph the linear function
• Use a ruler or other straightedge to draw a straight line through the points

Q: Can I use the slope-intercept form to find the equation of a line that is not a straight line?

A: No, the slope-intercept form is only used to find the equation of a straight line. If the line is not a straight line, you will need to use a different method to find its equation.