Question

find an equation for the line that passes through the points (1, -1) and (5, 5).

Explanation:

Step1: Calculate the slope

Let $(x_1,y_1)=(1,-1)$ and $(x_2,y_2)=(5,5)$. Slope $m=\frac{y_2-y_1}{x_2-x_1}=\frac{5-(-1)}{5-1}=\frac{6}{4}=\frac{3}{2}$.

Step2: Use point-slope form

Point-slope formula: $y - y_1 = m(x - x_1)$. Substitute $m=\frac{3}{2}$, $x_1=1$, $y_1=-1$:
$y - (-1) = \frac{3}{2}(x - 1)$ → $y + 1 = \frac{3}{2}x - \frac{3}{2}$.

Step3: Simplify to slope-intercept form

Subtract 1 from both sides: $y = \frac{3}{2}x - \frac{3}{2} - 1$ → $y = \frac{3}{2}x - \frac{5}{2}$.

Answer:

$y = \frac{3}{2}x - \frac{5}{2}$