Question

1. fill in the requested info:

slope-intercept form
point-slope form
slope formula
standard form
write the linear equation in slope-intercept form given the following:

1. slope = $\frac{-2}{9}$ and y-intercept = -5
2. slope = 10 and y-intercept = 8
3. graph
4. graph
5. $x - 6y = -12$
6. $5x + 4y = 20$
7. slope = $\frac{-4}{3}$ and $(-9, 17)$
8. $(-6, -4)$ and $(12, 11)$

Explanation:

Problem 2:

Step1: Recall slope - intercept form

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

Step2: Substitute the values

We are given that $m=\frac{-2}{9}$ and $b = - 5$. Substituting these values into the slope - intercept form, we get $y=\frac{-2}{9}x-5$.

Step1: Recall slope - intercept form

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

Step2: Substitute the values

We are given that $m = 10$ and $b=8$. Substituting these values into the slope - intercept form, we get $y = 10x+8$.

Step1: Identify two points on the line

From the graph, we can see that the line passes through $(0,5)$ (the y - intercept) and $(4,4)$.

Step2: Calculate the slope

The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Using the points $(0,5)$ and $(4,4)$, we have $m=\frac{4 - 5}{4-0}=\frac{-1}{4}$.

Step3: Write the equation

The slope - intercept form is $y=mx + b$. We know that $b = 5$ (from the point $(0,5)$) and $m=-\frac{1}{4}$. So the equation is $y=-\frac{1}{4}x + 5$.

Answer:

$y =-\frac{2}{9}x - 5$

Problem 3: