Question

suppose (-5, -8) and (15, 16) are two points on a line. find another point on the line.

Explanation:

Step1: Calculate the slope

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(-5,-8)$ and $(x_2,y_2)=(15,16)$. Then $m=\frac{16-(-8)}{15 - (-5)}=\frac{16 + 8}{15+5}=\frac{24}{20}=\frac{6}{5}$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Let's use the point $(-5,-8)$ and $m = \frac{6}{5}$. Then $y+8=\frac{6}{5}(x + 5)$.

Step3: Find a new point

Let $x = 0$. Then $y+8=\frac{6}{5}(0 + 5)$. So $y+8=6$, and $y=-2$.

Answer:

$(0,-2)$