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Chapter 1: Problem 64

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. $$6 x-5 y-20=0$$

Short Answer

Expert verified
The slope-intercept form is \(y = 1.2x - 4\). The slope is \(1.2\) and the y-intercept is \(-4\). See the graph for the representation of the linear equation.

Step by step solution

01

Convert to slope-intercept form

Rewrite \(6x - 5y - 20 = 0\) to slope-intercept form \(y = mx + b\). To do this, isolate y by working out the equation as follows: firstly, subtract \(6x\) from both sides, which gives \(-5y = -6x + 20\). Then divide every term by -5. This gives \(y = 1.2x - 4\).
02

Identify the slope and y-intercept

Evaluate the equation \(y = 1.2x - 4\). The coefficient of x is the slope and the constant is the y-intercept. Thus, the slope is \(1.2\) and the y-intercept is \(-4\).
03

Graph the linear function

To plot the graph, start at the y-intercept which is \(-4\). Then, using the slope, rise up 1.2 units and run 1 unit to the right. Plot this new point. Continue this process to get enough points. All these points will be aligned and can be connected to graph the linear equation.

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