Question

a line passes through the points (-5, 7) and (4, 13). using the point (-5, 7), write an equation for the line in point - slope form. (y - □) = □(x - □)

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2-y_1}{x_2-x_1}$. Substitute $(x_1,y_1)=(-5,7)$ and $(x_2,y_2)=(4,13)$:
$m=\frac{13-7}{4-(-5)}=\frac{6}{9}=\frac{2}{3}$

Step2: Apply point-slope form

Point-slope form is $y-y_1=m(x-x_1)$. Use $(x_1,y_1)=(-5,7)$ and $m=\frac{2}{3}$:
$y-7=\frac{2}{3}(x-(-5))$
Simplify the $x$-term: $y-7=\frac{2}{3}(x+5)$

Answer:

$\boldsymbol{y-7=\frac{2}{3}(x-(-5))}$ or simplified as $\boldsymbol{y-7=\frac{2}{3}(x+5)}$