Problem 63 - Precalculus Essentials

Question

a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. $$8 x-4 y-12=0$$

Step-by-Step Solution

Answer

The slope intercept form of the equation is \(y = 2x - 3\). The slope is 2 and the y-intercept is -3. To graph, start at the point (0, -3) and then go up 2 units and right 1 unit, then draw the line through these points.

Step 1: Rewrite in slope-intercept form

To rewrite \(8x - 4y -12 =0\) in slope-intercept form, isolate \(y\) on one side of the equation. This can be achieved by first subtracting \(8x\) from both sides, to get \(-4y = -8x + 12\). Then divide through by \(-4\) to get \(y = 2x -3\).

Step 2: Identify the slope and y-intercept

The form \(y = mx + b\) gives us \(m\) as the slope and \(b\) as the y-intercept. From the equation \(y = 2x -3\), we can see that the slope \(m\) is 2 and the y-intercept \(b\) is -3.

Step 3: Graph the linear function

First plot the y-intercept on the vertical axis at \(y = -3\). Then from this point, use the slope to find the next point on the line. The slope is 2, which as a fraction is \(2/1\), meaning move up 2 units and right 1 unit. Draw the line through these two points.