Question

write the equation of the line that passes through the points (7, 8) and (0, -8). put your answer in fully simplified point - slope form, unless it is a vertical or horizontal line.

Explanation:

Step1: Calculate 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 \((x_2,y_2)=(0, - 8)\). So \( m=\frac{-8 - 8}{0 - 7}=\frac{-16}{-7}=\frac{16}{7} \).

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 \((0,-8)\) (which is the y - intercept, but we can use any of the two points). Using \((x_1,y_1)=(0,-8)\) and \( m = \frac{16}{7} \), we get \( y-(-8)=\frac{16}{7}(x - 0) \), which simplifies to \( y + 8=\frac{16}{7}x \). We can also use the point \((7,8)\). Then \( y - 8=\frac{16}{7}(x - 7) \).

Answer:

\( y - 8=\frac{16}{7}(x - 7) \) (or \( y + 8=\frac{16}{7}x \))