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Chapter 1: Problem 22

Find the slope and \(y\) -intercept (if possible) of the equation of the line. Sketch the line. $$3 y+5=0$$

Short Answer

Expert verified
The slope of the line is 0, and the y-intercept is -5/3.

Step by step solution

01

Write the equation in slope-intercept form

To do this, isolate y in the equation. Using the equation \(3y + 5 = 0 \), subtract 5 from both sides of the equation, which yields \(3y = -5 \). Then, divide both sides of the equation by 3. The result is \(y = -5/3 \). The number -5/3 is the y-intercept which is the 'c' term in the slope-intercept form of the equation.
02

Find the slope

Since there is no x term in the equation, the slope 'm' is 0. So the slope of the line is 0.
03

Sketch the Line

The slope is 0, which means the line is horizontal. The y-intercept is -5/3, which is where the line crosses the y-axis. We plot a point at \(y = -5/3\) on the vertical (y) axis, then draw a horizontal straight line through that point. It is a horizontal line parallel to the x-axis at y = -5/3.

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