Question

using a line to find a point - slope equation
what is the equation of the line in point - slope form?
$y + 4=\frac{1}{2}(x + 4)$
$y - 4=\frac{1}{2}(x + 4)$
$y - 0 = 2(x - 4)$
$y - 4 = 2(x - 0)$

Explanation:

Step1: Identify two points on line

Points: $(4, 0)$ and $(-4, -4)$

Step2: Calculate the slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{-4-0}{-4-4}=\frac{-4}{-8}=\frac{1}{2}$

Step3: Recall point-slope form

Point-slope form: $y-y_1=m(x-x_1)$

Step4: Substitute point $(-4,-4)$ and $m$

$y-(-4)=\frac{1}{2}(x-(-4))$
Simplify: $y+4=\frac{1}{2}(x+4)$

Answer:

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