Question

a line passes through the point (8, -2) and has a slope of $-\frac{3}{2}$. write an equation in slope-intercept form for this line.

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept. We know that $m =-\frac{3}{2}$, and the line passes through the point $(x,y)=(8,-2)$.

Step2: Substitute into the equation to find $b$

Substitute $x = 8$, $y=-2$ and $m=-\frac{3}{2}$ into $y=mx + b$:

$$
LATEXBLOCK0
$$

Step3: Solve for $b$

Add 12 to both sides of the equation:

$$
LATEXBLOCK1
$$

Step4: Write the equation

Now that we know $m =-\frac{3}{2}$ and $b = 10$, substitute these values into the slope - intercept form $y=mx + b$.
We get $y=-\frac{3}{2}x+10$.

Answer:

$y =-\frac{3}{2}x + 10$