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Chapter 1: Problem 60

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. $$4 x+y-6=0$$

Short Answer

Expert verified
The slope-intercept form of the given equation is \(y = -4x + 6\). The slope is -4 and the y-intercept is 6. A graph of this linear function would start at the point (0,6) on the y-axis and fall, going down by 4 units for each unit moved to the right.

Step by step solution

01

Rewrite in Slope-Intercept Form

To convert the given equation \(4x + y - 6 = 0\) into slope-intercept form, isolate y. We do this by moving the terms involving x to the other side of the equation. So, we get: \(y = -4x + 6\)
02

Identify the Slope and Y-intercept

In the slope-intercept form, the coefficient of x is the slope \(m\) and the constant term is the y-intercept \(c\). From the equation \(y = -4x + 6\), we can see that the slope \(m = -4\) and the y-intercept \(c = 6\).
03

Graph the Function

We can now use the slope and y-intercept to graph the linear function. First plot the y-intercept on the y-axis at the point (0,6). The slope of -4 means that for each positive step in x, y decreases by 4. Thus, from the y-intercept, we can move to the right by 1 and down by 4 to get another point on the line. Join these two points to graph the line.

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