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Chapter 1: Problem 59

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. $$3 x+y-5=0$$

Short Answer

Expert verified
The equation in slope-intercept form is \( y = -3x + 5 \). The slope is \(-3\) and the y-intercept is \(5\).

Step by step solution

01

Rewrite in Slope-Intercept Form

The first task is to change the equation \(3x + y - 5 = 0\) into slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. Add \( -3x \) to both sides of the equation to get \( y = -3x + 5 \).
02

Identify the Slope and Y-Intercept

Now, in the slope-intercept form, from the equation \( y = -3x + 5 \), you can easily identify that the slope \(m\) is \(-3\) and the y-intercept \(b\) is \(5\).
03

Graph the Linear Function

To graph the linear function, first plot the y-intercept \(5\) on the y-axis. The slope \(-3\) can be understood as \(-3/1\); this means for every one step to the right on the x-axis, move three steps downwards. Following this method, plot more points. Finally, draw a line passing through these points, and that would be the graph of the function \( y = -3x + 5 \).

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Most popular questions from this chapter

Find and simplify the difference quotient $$\frac{f(x+h)-f(x)}{h}, h \neq 0$$for the given function. $$f(x)=\frac{1}{x}$$

$$\text { Solve and check: } \frac{x-1}{5}-\frac{x+3}{2}=1-\frac{x}{4}$$

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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The function \(f(x)=5\) is one-to-one.
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