Question

graph the line that passes through the points (-8, -4) and (-9, -4) 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 \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Here, \((x_1, y_1) = (-8, -4)\) and \((x_2, y_2) = (-9, -4)\). So, \( m = \frac{-4 - (-4)}{-9 - (-8)} = \frac{0}{-1} = 0 \).

Step2: Determine the equation of the line

A line with slope \( m = 0 \) is a horizontal line. The equation of a horizontal line passing through a point \((x, y)\) is \( y = y_0 \), where \( y_0 \) is the y - coordinate of the point. Since both points have a y - coordinate of - 4, the equation of the line is \( y=-4 \).

Step3: Graph the line

To graph the line, we plot the points \((-8, -4)\) and \((-9, -4)\) on the coordinate plane. Then we draw a horizontal line passing through these points (since the slope is 0, the line is horizontal and parallel to the x - axis, with all points on the line having a y - coordinate of - 4).

Answer:

The equation of the line is \( y = - 4 \), and the line is a horizontal line passing through the points \((-8, -4)\) and \((-9, -4)\) (parallel to the x - axis with \( y=-4 \) for all x - values).