Mathematics Homework Solutions and Graphs

This document provides solutions and graphs for linear equations in two variables, slope-intercept form, intercepts, and more for Mathematics homework. It includes tables, graphs, and equations for each problem. The subject is Mathematics and the course code, name, and college/university are not mentioned.

Mathematics Homework
Student’s Name
Institution Affiliation
1

1. Graph the linear equation in two variables. Find at least five solutions in the table of values for the
equation and graph the line.
x (x, y)
-2 4 (-2, 4)
-1 1 (-1, 1)
0 -2 (0, -2)
1 -5 (1,-5)
2 -8 (2,-8)
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-10
-8
-6
-4
-2
0
2
4
6
(-2, 4)
(-1, 1)
(0, -2)
(1, -5)
(2, -8)
f(x) = − 3 x − 2
2

2. Find the equation of the line shown. The equation will be x=−3
3. Graph the linear equation using the slope and y-intercept.
y−intercept =1
While slope= 2
5: this shows that the slope of equation is positive. This indicates a change of x
by 5 units and the value of y change by 2 units from the y-intercept. This means the co ordinates of the
line will be (0,1) and (5,3).
3

0 1 2 3 4 5 6
0
0.5
1
1.5
2
2.5
3
3.5
(0, 1)
(5, 3)
f(x) = 0.4 x + 1
5 Units
2 Unints
4. Graph the linear equation using the slope and y-intercept.
y−intercept =0
slope=−4
3 , this shows that the slope of equation is negative. This indicates a change of x
by negative -3 units and the value of y change by 4 units from the y-intercept. This means the co
ordinates of the line will be (0,0) and (-3,4).
-3.5 -3 -2.5 -2 -1.5 -1 -0.5 0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
(0, 0)
(-3, 4) 3
Units
4 Units
x
4

5. Consider the equation:
A. Put the equation in the slope-intercept form:
To obtain the slope-intercept form, you need to make y the subject of the formula
y= 3
4 x +2
B. Identify the slope: 3
4
C. Identify the y-intercept: 2
D. Graph the line.
-3 -2.5 -2 -1.5 -1 -0.5 0
0
0.5
1
1.5
2
2.5
(0, 2)
(-2.67, 0)
f(x) = 0.749063670411985 x + 2
6. Use the intercepts to graph the equation.
Intercepts are y and x intercepts, which are obtained when x=0 or y = 0, respectively.
x 0 -5
y 0.
5
0
5

-6 -5 -4 -3 -2 -1 0
0
0.1
0.2
0.3
0.4
0.5
0.6
(0, 0.5)
(-5, 0)
f(x) = 0.1 x + 0.5
7. Graph both linear equations in the same rectangular coordinate system. Decide if the lines are parallel,
perpendicular or neither parallel nor perpendicular.
The be equation will be graphed using the intercepts.
First equation
x -5 0 -4
y 1 -4 0
Second equation
x -1 0 -6
y 5 6 0
6

-7 -6 -5 -4 -3 -2 -1 0
-6
-4
-2
0
2
4
6
8
(-1, 5)
(0, 6)
-(6, 0)
(0, -4)
(-4, 0)
(-6, 2)
f(x) = x + 6
f(x) = − x − 4
The two lines are neither parallel nor perpendicular.
7

Graph both linear equations in the same rectangular coordinate system. Decide if the lines are parallel,
perpendicular or neither parallel nor perpendicular.
-5 -4 -3 -2 -1 0 1 2 3 4 5
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
(0, 2)
(-4, 0)
(0, -2)
(4, 0)
f(x) = 0.5 x + 2
f(x) = 0.5 x − 2
The two lines are perpendicular.
8