write an equation of the line that passes through the pair of points. use improper fractions in your…

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(5,-3)$ and $(x_2,y_2)=(2,5)$. Then $m=\frac{5 - (-3)}{2 - 5}=\frac{5 + 3}{-3}=-\frac{8}{3}$.

Step2: Use the point - slope form

The point - slope form is $y - y_1=m(x - x_1)$. Using the point $(2,5)$ and $m =-\frac{8}{3}$, we have $y - 5=-\frac{8}{3}(x - 2)$.

Step3: Convert to slope - intercept form

Expand the right side: $y-5=-\frac{8}{3}x+\frac{16}{3}$. Add 5 to both sides: $y=-\frac{8}{3}x+\frac{16}{3}+5$. Since $5=\frac{15}{3}$, then $y=-\frac{8}{3}x+\frac{16 + 15}{3}=-\frac{8}{3}x+\frac{31}{3}$.

Answer:

$y =-\frac{8}{3}x+\frac{31}{3}$