Question

find an equation for the line that passes through the points (4, -4) and (-2, 4).

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Let $(x_1,y_1)=(4,-4)$ and $(x_2,y_2)=(-2,4)$.
$m=\frac{4-(-4)}{-2-4}=\frac{8}{-6}=-\frac{4}{3}$

Step2: Use point-slope form

Point-slope form: $y-y_1=m(x-x_1)$. Use $(x_1,y_1)=(4,-4)$.
$y-(-4)=-\frac{4}{3}(x-4)$

Step3: Simplify to slope-intercept form

Simplify the equation:
$y+4=-\frac{4}{3}x+\frac{16}{3}$
$y=-\frac{4}{3}x+\frac{16}{3}-4$
$y=-\frac{4}{3}x+\frac{16}{3}-\frac{12}{3}$
$y=-\frac{4}{3}x+\frac{4}{3}$

Step4: Convert to standard form (optional)

Multiply by 3 to eliminate fractions:
$3y=-4x+4$
$4x+3y=4$

Answer:

$y=-\frac{4}{3}x+\frac{4}{3}$ (or $4x+3y=4$)