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Chapter 1: Problem 27

Find the \(x\) - and \(y\) -intercepts of the graph of the equation. $$y=|3 x-7|$$

Short Answer

Expert verified
The x-intercept is at \(x = 7/3\) and the y-intercept is at \(y = 7\).

Step by step solution

01

Find the x-intercept(s)

Set \(y = 0\) and solve the equation for \(x\). \n\[\n0 = |3x - 7|\n\]\nDetails: The value inside the absolute bars can either be negative or positive to make the absolute value 0. Hence, set up two equations \(3x - 7 = 0\) and \(-(3x - 7) = 0\). Solving these equations will get the x-intercept(s).
02

Solve the equations for x

For the equation \(3x - 7 = 0\), solving for \(x\) gives \(x = 7/3\). For the equation \(-(3x - 7) = 0\), solving for \(x\) gives \(x = 7/3\). Thus, there is only one x-intercept at \(x = 7/3\).
03

Find the y-intercept

Set \(x = 0\) and calculate the value for \(y\). \n\[\n y = |3*0 - 7| = |-7| = 7\n\]\nSo the y-intercept is at \(y = 7\).

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