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Chapter 3: Problem 82

Explain how to graph \(A x+B y=C\) if \(C\) is not equal to zero.

Short Answer

Expert verified
First set \(y = 0\) to find the x-intercept (\(C/A\),0), then set \(x = 0\) to find the y-intercept (0, \(C/B\)). Finally, plot these points on a graph, and connect them with a straight line.

Step by step solution

01

Understanding the Equation

Given the equation \(A x + B y = C\), this standard form of a linear equation simplifies the process of finding the x and y intercepts. X-intercepts occur when \(y = 0\), and Y-intercepts occur when \(x = 0\). These intercepts are crucial as they provide two points through which the line passes. Before moving ahead, also note that \(C\) 鈮� \(0\) as per the problem statement.
02

Finding the X-Intercept

To find the x-intercept, set \(y = 0\) in our given equation and then solve for \(x\). This gives: \(Ax + B(0) = C\). Simplifying this gives \(x = C/A\).
03

Finding the Y-Intercept

To find the y-intercept, set \(x = 0\) in our given equation and then solve for \(y\). This gives: \(A(0) + By = C\). Simplifying this gives \(y = C/B\).
04

Plotting the Line

Now that we have the x-intercept (\(C/A\),0) and the y-intercept (0, \(C/B\)), plot these two points on the coordinate plane. Draw a line through these two points; this is the graph of the given equation \(A x + B y = C\).

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Will help you prepare for the material covered in the first section of the next chapter. Is \((-4,3)\) a solution of both \(x+2 y=2\) and \(x-2 y=6 ?\)

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