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Chapter 11: Chapter 11

Problem 222

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Find the slope, the \(\mathrm{y}\) -intercept, and the \(\mathrm{x}\) -intercept of the equation \(2 x-3 y-18=0\)

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The slope of the equation is \(m = \frac{2}{3}\), the y-intercept is \(b = -6\), and the x-intercept is \(x = 9\).
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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Rewrite the equation in slope-intercept form (y = mx + b)

To write the given equation in slope-intercept form (y = mx + b), we need to first move the 3y term to the other side and then divide each term by 3: \(2x - 3y - 18 = 0\) Add 3y to both sides and get: \(2x - 18 = 3y\) Now divide each term by 3: \(y = \frac{2}{3}x - 6\)

Step 2: Determine the slope and y-intercept

In the equation we obtained in Step 1, the slope (m) is the coefficient of the x term, and the y-intercept (b) is the constant term. From the equation: \(y = \frac{2}{3}x - 6\) The slope (m) is: \(m = \frac{2}{3}\) The y-intercept (b) is: \(b = -6\)

Step 3: Determine the x-intercept

To find the x-intercept, we set the value of y to 0 and solve for x: \(\frac{2}{3}x - 6 = 0\) Add 6 to both sides: \(\frac{2}{3}x = 6\) Now multiply both sides by \(\frac{3}{2}\) to solve for x: \(x = \frac{3}{2} \cdot 6\) \(x = 9\) The x-intercept is 9. So, the slope of the equation is \(\frac{2}{3}\), the y-intercept is -6, and the x-intercept is 9.

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