Applied Finite Mathematics by Rupinder Sekhon, UniqU, LLC - HTML preview

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Chapter 2Linear Equations: Homework

GRAPHING A LINEAR EQUATION

Work the following problems.

Is the point (2, 3) on the line 5x−2y=4?

Yes
Exercise 2.

Is the point (1, – 2) on the line 6x−y=4?

For the line 3x−y=12, complete the following ordered pairs.

(2, ) ( , 6)

(0, ) ( , 0)

(2, –6) (6, 6)

(0,–12) (4, 0)

Exercise 4.

For the line 4x+3y=24, complete the following ordered pairs.

(3, ) ( , 4)

(0, ) ( , 0)

Graph y=2x+3

The line y=2x+3 passing through the points (-1,1) and (0,3) on a Cartesian graph.
Figure 2.0
Exercise 6.

Graph y=−3x+5

Graph y=4x−3

The line y=4x-3 passing through the points (0,-3) and (2,5) on a Cartesian graph.
Figure 2.0
Exercise 8.

Graph x−2y=8

Graph 2x+y=4

The line 2x+y=4 passing through the point (0,4) and (2,0) on a Cartesian graph.
Figure 2.0
Exercise 10.

Graph 2x−3y=6

Graph 2x+4=0

A line passing through the point (-2,0) on a Cartesian graph.
Figure 2.0
Exercise 12.

Graph 2y−6=0

Graph the following three equations on the same set of coordinate axes.

(2.1)y=x+1   y=2x+1  y=−x+1
The lines y=-x+1, y=2x+7, and y=x+1 intersecting at the point (0,1) on a Cartesian graph.
Figure 2.0
Exercise 14.

Graph the following three equations on the same set of coordinate axes.

(2.2)y=2x+1  y=2x  y=2x−1

Graph the line using the parametric equations

(2.3)
_autogen-svg2png-0015.png
A line passing through the points (-5,0), (1,3), and (3,4) on a Cartesian graph.
Figure 2.0
Exercise 16.

Graph the line using the parametric equations

(2.4)x=2−3t,   y=1+2t

SLOPE OF A LINE

Find the slope of the line passing through the following pair of points.

(2, 3) and (5, 9)

(2.5)m=2
Exercise 18.

(4, 1) and (2, 5)

(– 1, 1) and (1, 3)

(2.6)m=1
Exercise 20.

(4, 3) and (– 1, 3)

(6, – 5) and (4, – 1)

(2.7)m=−2
Exercise 22.

(5, 3) and (– 1, – 4)

(3, 4) and (3, 7)

(2.8)m=undefined
Exercise 24.

(– 2, 4) and (– 3, – 2)

(– 3, – 5) and (– 1, – 7)

(2.9)m=−1
Exercise 26.

(0, 4) and (3, 0)

Determine the slope of the line from the given equation of the line.

(2.10)y=−2x+1
(2.11)m=−2
Exercise 28.

y=3x−2

(2.12)2x−y=6
(2.13)m=2
Exercise 30.
(2.14)x+3y=6
(2.15)3x−4y=12
(2.16)m=3/4
Exercise 32.

What is the slope of the x-axis? How about the y-axis?

Graph the line that passes through the given point and has the given slope.

(1, 2) and m=−3/4

A line passing through the points (1,2) and (5,-1) on a Cartesian graph.
Figure 2.0
Exercise 34.

(2, –1) and m=2/3

(0, 2) and m=−2

A line passing through the points (0,2) and (1,0) on a Cartesian graph.
Figure 2.0
Exercise 36.

(2, 3) and m=0

DETERMINING THE EQUATION OF A LINE

Write an equation of the line satisfying the following conditions. Write the equation in the form _autogen-svg2png-0034.png.

It passes through the point (3, 10) and has slope=2.

(2.17)y=2x+4
Exercise 38.

It passes through the point (4,5) and has m=0.

It passes through (3, 5) and (2, – 1).

(2.18)y=6x−13
Exercise 40.

It has slope 3, and its y-intercept equals 2.

It passes through (5, – 2) and m=2/5.

(2.19)y=2/5x−4
Exercise 42.

It passes through (– 5, – 3) and (10, 0).

It passes through (4, – 4) and (5, 3).

(2.20)y=7x−32
Exercise 44.

It passes through (7, – 2) and its y-intercept is 5.

It passes through (2, – 5) and its x-intercept is 4.

(2.21)y=5/2x−10
Exercise 46.

Its a horizontal line through the point (2, – 1).

It passes through (5, – 4) and (1, – 4).

(2.22)y=−4
Exercise 48.

It is a vertical line through the point (3, – 2).

It passes through (3, – 4) and (3, 4).

(2.23)x=3
Exercise 50.

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