MAT 1100 Quantitative Reasoning: Module 3 Lesson 1 Assignment 2

This document provides a comprehensive solution to the MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2. The assignment covers key concepts in linear equations and their graphical representations. The solution includes completing ordered pairs, graphing linear equations, finding x and y intercepts, and determining the slope of a line. The assignment also explores concepts like parallel lines, and average rate of change in a population. Detailed step-by-step solutions are provided for each problem, including the identification of the slope (positive, negative, zero, or undefined), and the calculation of the pitch of a roof. The document also features graphical representations of the equations, aiding in the visualization and understanding of the concepts.

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
Student Name:
1) Given the equation
y = x - 5
a) Complete the ordered pairs. Find the missing coordinate.
(0, ), ( , 0), (4, )
Solution: Since y = x – 5,
When x = 0, y = 0 -5 = -5
Hence, coordinate is (0, -5).
When y = 0, 0 = x – 5, this gives x = 5
Hence, coordinate is (5, 0).
When x = 4, y = 4 – 5, this gives y = -1
Hence, coordinate is (4, -1).
b) Graph the equation. Use at least two of the points completed above.
A) B)
C) D)

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
Solution:
Hence, answer option (D) is correct.
Find the intersections of x and y for the equation if they exist. Otherwise, write none. Then graph the
equation.
2) 12y - 3x = -9
a) x-intercept:
b) y-intercept:
Solución(a): Sincé 12y -3x = -9
For x – intercept, substitute y = 0 we get
Solución(b): Sincé 12y -3x = -9
For y – intercept, substitute x = 0 we get

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
c) Graph the equation.
A) B)
C) D)
Solution:

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
Hence, answer option (B) is correct.
3) y – 5 = 0
a) x-intercept
b) y-intercept:
Solution (a): Since, y – 5 = 0, this gives y = 5. Hence, x – intercpt : None.
Solution (b): Since, y – 5 = 0, this gives y = 5. Hence, y - intercept is 5
c) Graph the equation.
A) B)

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
C) D)
Solution: The graph of the function y – 5 = 0 is
4) Identify whether the slope is positive, negative, zero, or undefined.
a) ____Positive_____________ b) ______0_________ c) __Negative______________

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
5) Find the slope of the line through the points. Use the slope formula.
(-4, 3) and (-3, 4)
Solution: The slope of the line passing through the points and is
So, the slope of the line passing through the points (-4, 3) and (-3, 4) is
Decide whether the pair of lines is parallel, perpendicular, or neither.
6) The line through (6, 4) and (12, 4) and the line through (-8, -1) and (-5, -1)
.Solution: Suppose and are the slopes of line, then
(a) Lines are parallel if
(b) Lines are perpendicular if
(c) Otherwise lines are neither parallel nor perpendicular.
Now, the slope of line passing through (6, 4) and (12, 4) is
The slope of line passing through (-8, -1) and (-5, -1) is

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
Since, slopes are equal, the lines are parallel.
7) The pitch of a roof is its slope( rise
run ). Find the pitch of the roof shown.
Solution: The pitch of the roof is slope
8) In 1980, the population of a city was 5.3 million. By 1992 the population had grown to 6.9 million. Find the
average rate of change in the population. The average rate of change is an application of the concept slope
( C h ange ∈y
C h ange∈x )
Solution: The rate of change in the population is

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
9) Find the average rate of change. Use appropriate units.
Solution: The two points on the line are . The averages rate of changes the
slope of the line. So, the average rate of change is
10) Graph the following line.
a) Through (4, -1), m =−3
4
A) B)

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
C) D)
Solution: The equation of line passing through
(4, -1) with slope is
And the graph of the line is

MAT 1100 Quantitative Reasoning Module 3 Lesson 1 Assignment 2
Hence, answer option (C) is correct.