Math Homework: Graphing Linear Equations, Intercepts, and Slopes

This mathematics homework assignment focuses on linear equations and their graphical representations. The solution includes detailed steps for graphing linear equations using tables of values, finding equations of lines, and graphing using slope and y-intercepts. The document covers various aspects of linear equations, including putting equations in slope-intercept form, identifying slopes and y-intercepts, and graphing lines using intercepts. Furthermore, the assignment explores the relationships between lines, determining whether they are parallel, perpendicular, or neither, by graphing multiple equations on the same coordinate system. The solutions provide clear explanations and visual representations to aid understanding of the concepts.

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