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Chapter 1: Q. 72 (page 42)

Find the slope and y-intercept of each line. Graph the line by hand. Verify using a graphing utility.

y=-3x+4

Short Answer

Expert verified

Slope is-3

y-intercept is(0,4)

The graph is

Verification:

Both graphs are the same.

Step by step solution

01

Step 1. Given information

The equation of a line is

y=-3x+4

02

Step 2. Finding the slope of line and y-intercept

The equation of line is y=-3x+4

Compare with slope-intercept formula of a line

y=mx+b

So,

m=-3b=4

Therefore,

slope is -3

y-intercept is(0,4)

03

Step 3. Graphing the line by hand

Firstly, we can make a table of x and y values by selecting some random values of x and find y

x
y=-3x+4
-1
7
0
4
1
1

Locate points (-1,7),(0,4),(1,1)on the graph and join them to get the equation of line.

04

Step 4. Verify graph using the graphing utility

The graph by hand is

The graph using a calculator is

Here, both graphs are the same.

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Most popular questions from this chapter

Tell whether the given points are on the graph of the equation.

Equation:y=x3-2xPoints:(0,0);(1,1);(1,-1)

Determine the coordinates of the points shown. Tell in which quadrant each point lies. Assume the coordinates are integers.

Show that the line containing the points (a, b) and (b, a), a b, is perpendicular to the line y = x. Also show that the midpoint of (a, b) and (b, a) lies on the line y = x.

Can the equation of every line be written in slope鈥搃ntercept form? Why?

True or FalseVertical lines have an undefined slope.
See all solutions

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