Question

1. the line passes thru (18,15) and (23,11)

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(18,15)$ and $(x_2,y_2)=(23,11)$. Then $m=\frac{11 - 15}{23 - 18}=\frac{-4}{5}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(18,15)$ and $m =-\frac{4}{5}$, we have $y - 15=-\frac{4}{5}(x - 18)$.

Step3: Expand and simplify

$y-15=-\frac{4}{5}x+\frac{72}{5}$. Then $y=-\frac{4}{5}x+\frac{72}{5}+15$. $y=-\frac{4}{5}x+\frac{72 + 75}{5}=-\frac{4}{5}x+\frac{147}{5}$.

Answer:

The equation of the line is $y =-\frac{4}{5}x+\frac{147}{5}$