Question

what is an equation of the line that passes through the points (2, 8) and (-8, -7)?

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let \( (x_1, y_1)=(2, 8) \) and \( (x_2, y_2)=(-8, -7) \). Then \( m=\frac{-7 - 8}{-8 - 2}=\frac{-15}{-10}=\frac{3}{2} \).

Step2: Use point - slope form

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

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y - 8=\frac{3}{2}x-3 \). Then add 8 to both sides: \( y=\frac{3}{2}x - 3+8 \), so \( y=\frac{3}{2}x + 5 \). We can also write it in standard form \( 3x-2y=- 10 \) (by multiplying both sides of \( y=\frac{3}{2}x + 5 \) by 2 to get \( 2y = 3x+10 \), then rearranging to \( 3x-2y=-10 \)).

Answer:

The equation of the line is \( y=\frac{3}{2}x + 5 \) (or \( 3x - 2y=-10 \))