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Chapter 1: Problem 24

Find the slope and \(y\) -intercept (if possible) of the equation of the line. Sketch the line. $$2 x+3 y=9$$

Short Answer

Expert verified
The slope of the line is -2/3 and the y-intercept is 3. When sketched, the line will cross the y-axis at (0, 3) and slope downwards from left to right.

Step by step solution

01

Rewrite the equation in slope-intercept form

Start by isolating y. Do this by subtracting 2x from both sides of the equation. This results in the equation: \(3 y = -2x + 9\). Then, divide both sides by 3 to isolate y: \(y = -\frac{2}{3}x + 3\)
02

Identify the slope and y-intercept

The equation \(y = -\frac{2}{3}x + 3\) is now in slope-intercept form. The slope, or \(m\), is -2/3, which means that for every one unit the x-value increases, the y-value decreases by 2/3. The y-intercept, or \(b\), is 3, which is the point where the line crosses the y-axis.
03

Sketch the line.

Using the slope and y-intercept, start at the point (0, 3) on the y-axis. From there, remember that the slope is rise over run, so for each three units to the right that you move (the 'run'), move two units down (the 'rise'). This will give you points along the line that you can connect to get a visual of the line on the graph.

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