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Chapter 1: Q. 84 (page 42)

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

y=-1

Short Answer

Expert verified

Slope is0

y-intercept is(0,-1)

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=-1

02

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

The equation of the line is

y=-1

It can be written as

y=0-1y=0x-1

Compare with slope-intercept formula of a line

y=mx+b

So,

m=0b=-1

Therefore,

slope is 0

y-intercept is(0,-1)

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

y-value is always-1 for any x-values.

x
y
1
-1
2
-1
3
-1

Locate points(1,-1),(2,-1),(3,-1) on the graph and then join them to sketch the graph

04

Step 4. Verify graph using the graphing utility

The graph by hand is

The graph using calculator is

Here, both graphs are the same.

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Most popular questions from this chapter

Graph the line containing the point P and having slope m.

P(2,-4),m=0

Find the length of the line segment. Assume that the endpoints of each line segment have integer coordinates.

The tangent line to a circle may be defined as the line that intersects the circle in a single point, called the point of tangency. See the figure.

If the equation of the circle is x2+y2=r2and the equation of the tangent line is y = mx + b, show that:

(a) r2(1+m2)=b2

[Hint: The quadratic equation x2+(mx+b)2=r2has exactly one solution.]

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In Problem 17-36, solve each equation algebraically. Verify your solution using a graphing utility.

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