Question

graph the line that passes through the points (-8, 6) and (-6, 3) and determine the equation of the line.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). For points \((-8, 6)\) and \((-6, 3)\), we have \( x_1=-8, y_1 = 6, x_2=-6, y_2=3 \). So \( m=\frac{3 - 6}{-6-(-8)}=\frac{-3}{2}=-\frac{3}{2} \).

Step2: Use point - slope form to find the equation

The point - slope form of a line is \( y - y_1=m(x - x_1) \). Let's use the point \((-8, 6)\). Substitute \( m =-\frac{3}{2}, x_1=-8, y_1 = 6 \) into the formula:
\( y - 6=-\frac{3}{2}(x+8) \)
Expand the right - hand side: \( y - 6=-\frac{3}{2}x-12 \)
Add 6 to both sides: \( y=-\frac{3}{2}x-12 + 6=-\frac{3}{2}x-6 \)
(For graphing: Plot the points \((-8,6)\) and \((-6,3)\) on the coordinate plane. Then, using the slope \( -\frac{3}{2} \) (which means for every 2 units we move to the right along the x - axis, we move down 3 units), we can find more points on the line and draw a straight line through the plotted points.)

Answer:

The equation of the line is \( y =-\frac{3}{2}x-6 \) (To graph the line, plot the points \((-8,6)\) and \((-6,3)\) and draw a straight line passing through them using the slope to find additional points if needed).