Question

write an equation in slope - intercept form for the line that passes through the points (5, -14) and (10, -17).
y = \square x + \square

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(5,-14)$ and $(x_2,y_2)=(10,-17)$:
$m=\frac{-17-(-14)}{10-5}=\frac{-3}{5}$

Step2: Solve for y-intercept $b$

Use slope-intercept form $y=mx+b$, substitute $m=\frac{-3}{5}$ and $(x,y)=(5,-14)$:
$-14=\frac{-3}{5}(5)+b$
$-14=-3+b$
$b=-14+3=-11$

Step3: Write final equation

Substitute $m=\frac{-3}{5}$ and $b=-11$ into $y=mx+b$.

Answer:

$y = -\frac{3}{5}x - 11$