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. $(y - 7)=\frac{2}{3}(x - 5)$

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: Recall point-slope form

Point-slope form is $y-y_1=m(x-x_1)$. Substitute $m=\frac{2}{3}$, $x_1=-5$, $y_1=7$:
$y-7=\frac{2}{3}(x-(-5))$

Step3: Simplify the x-term

Rewrite $x-(-5)$ as $x+5$:
$y-7=\frac{2}{3}(x+5)$

Answer:

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