Question

a line passes through the point $(-4, 7)$ and has a slope of $\frac{3}{2}$. write an equation in slope - intercept form for this line.

Explanation:

Step1: Recall point-slope formula

The point-slope form is $y - y_1 = m(x - x_1)$, where $m=\frac{3}{2}$, $x_1=-4$, $y_1=7$.
$y - 7 = \frac{3}{2}(x - (-4))$

Step2: Simplify the right-hand side

Simplify the expression inside the parentheses.
$y - 7 = \frac{3}{2}(x + 4)$

Step3: Distribute the slope term

Multiply $\frac{3}{2}$ across the parentheses.
$y - 7 = \frac{3}{2}x + 6$

Step4: Solve for y (slope-intercept)

Add 7 to both sides to isolate y.
$y = \frac{3}{2}x + 6 + 7$
$y = \frac{3}{2}x + 13$

Answer:

$y = \frac{3}{2}x + 13$