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Linear Equations

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Problems:

Problem: 8/3.1
Y=2x+5
(8,y ), (-1,y), (x, -1)

Problem 70/3.1
Graph each equation. plot at least five points for each equation. use graph paper of a graphing calculator or excel

x-2y=6

x=6+2y

Problem 42/3.2

Graphing a line for given slope and a point
The line through (-2,3) with slope -2

Problem 52/3.2
Draw L1 through (-4,0) and (0,6). What is the slope of the line parallel to line L1.Draw L2 through the origin and parallel to L1.

Problem 32/3.3
x+2y=3
Find the y intercept.

Problem 72/3.3

y=x+7
y=-x+2

Determine whether lines are perpendicular or parrelel to each other.

Problem: 10/3.4

Write equation in slope intercept form

y+3=-3(x-6)

Problem: 24/3.4
Write the equation of a line which passes through (-1,-5) and has a slope =8

Problem: 56/3.4

Write the equation of the line which is parallel to -3x+2y=9 and contains the point (-2,1)

Problem: 62/3.4

The line passes through (3,2) and has a undefined slope

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Solution Summary

Solution to the various problems explains the steps for finding equation of line passing through given point and slope. It also explains how to determine whether given lines are parrelel or perpendicular to each other.

Solution Preview

Please refer attached files for better clarity of expressions and graphs.

Solutions:

Problem: 8/3.1

Y=2x+5

(8,y ), (-1,y), (x, -1)

Since points are lying on given line, they will satisfy the given equation.
Case1: (8,y)

y=2*8+5
y =21
Point is (8,21)

Case 2: (-1,y)

y= 2*(-1)+5=-2+5=3

Point is (-1,3)

Case 3: (x,-1)

-1=2x+5
Adding -5 both sides, we get
-1-5=2x+5-5
-6=2x
x=-3
Point is (-3,-1)

Problem 18/3.1

Y= -x+4
Information given can be written in the form of ordered pair as under:
(-2,y), (0,y), (2,y), (x,0), (x,-2)
Missing numbers are represented by x or y.

Case 1 : y=-x+4
(-2,y) lies on the given line, it will satisfy the given equation. So
y=2+4=6
Point is (-2,6)

Case 2:
y=-x+4
(0,y) lies on the given line, it will satisfy the given equation. So
y=0+4=4
Point is (0,4)

Case 3:
y=-x+4
(2,y) lies on the given line, it will satisfy the given equation. So
y=-2+4=2
Point is (2,2)

Case 4:
y=-x+4
(x,0) lies on the given line, it will satisfy the given equation. So
0=-x+4
Solving for x, we get
x=4
Point is (4,0)

Case 5:
y=-x+4
(x,-2) lies on the given line, it will satisfy the given equation. So
-2=-x+4
Solving for x, we get
x=6
Point is ...

Solution provided by:
Lokesh Jain, MSc
Education
  • BEng (Hons) , Birla Institute of Technology and Science, India
  • MSc (Hons) , Birla Institute of Technology and Science, India
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