Question

what is an equation of the line that passes through the points (-6, 6) and (-3, 1)?

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, \( x_1=-6,y_1 = 6,x_2=-3,y_2 = 1 \). So \( m=\frac{1 - 6}{-3-(-6)}=\frac{-5}{3} \).

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 \((-6,6)\). Substitute \( m =-\frac{5}{3},x_1=-6,y_1 = 6 \) into the formula: \( y - 6=-\frac{5}{3}(x + 6) \).

Step3: Simplify to slope - intercept form

Expand the right - hand side: \( y-6=-\frac{5}{3}x-10 \). Then add 6 to both sides: \( y=-\frac{5}{3}x-10 + 6=-\frac{5}{3}x-4 \).

Answer:

The equation of the line is \( y =-\frac{5}{3}x-4 \) (or in standard form \( 5x+3y=-12 \))