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Problem 222

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

Expert verified
The slope of the equation is $$m = \frac{2}{3}$$, the y-intercept is $$b = -6$$, and the x-intercept is $$x = 9$$.
See the step by step solution

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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