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Chapter 4: Q. 290 (page 519)

In the following exercises, use the graph to find the slope and y-intercept of each line. Compare the values to the equation y=mx+b.

y=-x+4

Short Answer

Expert verified

The slope of the line is m=-1and the y-intercept is (0,4).

Step by step solution

01

Step 1. Given information.

The given graph is:

The given equation is y=-x+4.

02

Step 2. Determine the slope and y-intercept from the graph.

Select any two points on the line. We'll use the points (0,4)and (4,0). Here, rise is 0-4=-4and run is 4-0=4.

m=RiseRun=-44=-1

The graph crosses the y-axis at (0,4), so the y-intercept of the graph is (0,4).

03

Step 3. Determine the slope and y-intercept from the equation.

On comparing y=-x+4and y=mx+b,

m=-1b=4

The slope is the same as the coefficient of x and the y-coordinate of the y-intercept is the same as the constant term.

04

Step 4. Conclusion.

The slope of the line is m=-1and the y-intercept is (0,4).

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Most popular questions from this chapter

An easy way to determine the slope of a roof is to set one end of a 12 inch level on the roof surface and hold it level. Then take a tape measure or ruler and measure from the other end of the level down to the roof surface. This will give you the slope of the roof. Builders, sometimes, refer to this as pitch and state it as an "x12 pitch" meaning x12, where xis the measurement from the roof to the level鈥攖he rise. It is also sometimes stated as an " x-in-12 pitch".

a) What is the slope of the roof in this picture?

b) What is the pitch in construction terms?

Explain in your own words why the slopes of two perpendicular lines must have opposite signs.

find an equation of a line parallel to the line y= -2x-3 and contains the point (-1,3). Write the equation in slope鈥搃ntercept form.

In the following exercises, find the x- and y-intercepts.

In the following exercises, graph each line with the given point and slope.

(2,3);m=-1
See all solutions

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