Question

write the equation of the line that passes through the points (7,8) and (9, -4). put your answer in fully simplified point - slope form, unless it is a vertical or horizontal line.

Explanation:

Step1: Find the slope

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( (x_1,y_1)=(7,8) \) and \( (x_2,y_2)=(9, - 4) \). So, \( m=\frac{-4 - 8}{9 - 7}=\frac{-12}{2}=-6 \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). We can use the point \( (7,8) \) (we could also use \( (9,-4) \)). Substitute \( m = - 6 \), \( x_1=7 \) and \( y_1 = 8 \) into the point - slope formula. We get \( y - 8=-6(x - 7) \).

Answer:

\( y - 8=-6(x - 7) \)