Analyzing Linear Equations: Graphing, Intersections, and Equations

This assignment focuses on linear equations, including creating tables of values, graphing lines, and finding points of intersection. It requires students to analyze linear and non-linear relations using difference tables and determine the equation of the lines. The assignment also involves graphing pairs of lines and identifying their intersection points. Finally, it prompts students to reflect on the clarity of the course material, identifying areas of confusion and well-presented concepts to improve the course. The assignment covers a range of fundamental algebraic concepts to enhance understanding of linear equations and their graphical representations.

ASSIGNMENT

1. Make a table of values for each of the following lines. Be sure to include negative
values of x in each. Draw one set of axes plot both lines on the same graph. Be sure to
fully label your graphs including axes, scale and the equations of the lines.
a. y=2 x−1
x y
-2 -5
-1 -3
0 -1
1 1
2 3
b. y=−3 x +9
x y
-2 15
-1 12
0 9
1 6
2 3
-2 -1 0 1 2 3
-10
-8
-6
-4
-2
0
2
4
6
8
10
x axis
y axis
2. Create a differences table for each of the following relations. Use this table to
determine if the relation is linear or non-linear. For the linear relations, develop the
equation of relations. You do not need to plot the lines.
a.
x y x difference y difference
4 2 +2 +1
6 3 +2 +1
8 4 +2 +1
10 5 +2 +1
12 6
y=2x-1
y=-3x+9

Sol. Linear
b.
x y x difference y difference
1 4 +2 +10
3 14 +2 +10
5 24 +2 +10
7 34 +2 +10
9 44
Sol. : Linear
c.
x y x difference y difference
-3 -3 -1 -2
-2 -1 -1 +2
-1 1 +1 +2
0 3 +1 +2
1 5
Sol. : Non-linear
d.
x y x difference y difference
-4 8 -2 +6
-2 2 -2 +2
0 0 +2 +2
2 2 +2 +6
4 8
Sol. Non-linear
3. Graph each pair of lines on the same set of axes. Determine the point of intersection
of two lines. Note that you may have to estimate the coordinates.
a. y=2 x−4∧ y=4 x+ 2
Sol.

-2 -1 0 1 2 3
-10
-8
-6
-4
-2
0
2
4
6
8
10
x axis
y axis
point of intersection: (-3,-10)
b. y=2 x−5∧ y=−x +7
Sol.
-2 -1 0 1 2 3
-10
-8
-6
-4
-2
0
2
4
6
8
10
x axis
y axis
Point of intersection (4,3)
4. On the four topics covered in this assignment, please tell us what in this course
material was least clear to you, and why. Also, if you found a particular item was
presented well for you, let us know. Your responses will help us improve the course.