Question

what is an equation of the line that passes through the points (-8, 5) and (-4, 0)?

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, \( x_1=-8,y_1 = 5,x_2=-4,y_2=0 \). So \( m=\frac{0 - 5}{-4-(-8)}=\frac{-5}{4}=-\frac{5}{4} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((-4,0)\) (we could also use \((-8,5)\)). Substitute \( m =-\frac{5}{4},x_1=-4,y_1 = 0 \) into the formula: \( y-0=-\frac{5}{4}(x + 4) \).

Step3: Simplify the equation

Simplify \( y=-\frac{5}{4}x-5 \). We can also write it in standard form \( 5x+4y=-20 \) or slope - intercept form \( y =-\frac{5}{4}x - 5 \).

Answer:

The equation of the line is \( y=-\frac{5}{4}x - 5 \) (or \( 5x + 4y=-20 \))