Question

which equation is a point slope form equation for line ab?\
\bigcirc $y + 1 = -\frac{2}{3}(x - 4)$\
\bigcirc $y + 1 = \frac{3}{2}(x - 4)$\
\bigcirc $y + 1 = \frac{2}{3}(x - 4)$\
\bigcirc $y + 1 = -\frac{3}{2}(x - 4)$\
(there is a coordinate grid with line ab and points a, b marked)

Explanation:

Step1: Identify points on line

Point $A=(4, -1)$, Point $B=(1, 2)$

Step2: Calculate slope $m$

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$m=\frac{2-(-1)}{1-4}=\frac{3}{-3}=-\frac{3}{2}$

Step3: Apply point-slope form

Point-slope formula: $y-y_1=m(x-x_1)$, use point $A$
$y-(-1)=-\frac{3}{2}(x-4)$
Simplify to: $y+1=-\frac{3}{2}(x-4)$

Answer:

$y+1=-\frac{3}{2}(x-4)$ (the fourth option)