Linear Functions: Solving Problems and Equations - MAP4C Assignment

This assignment focuses on exploring the characteristics of linear functions within the context of a high school mathematics course (MAP4C). The assignment is divided into two main parts: Part A involves determining the truth value of statements related to linear equations, slopes, and intercepts, requiring students to provide justifications for their answers. Part B presents problem-solving scenarios where students are tasked with calculating slopes, writing equations in various forms (including standard form), and graphing linear functions based on given information like points and intercepts. The assignment covers key concepts such as slope calculation, finding x and y intercepts, and the relationship between equations and their graphical representations. Students are expected to demonstrate their understanding of these concepts through calculations, explanations, and graphical representations.

Lesson 11 Assignment
In this assignment you are going to explore the characteristics of linear functions.
Make sure you answer all questions in the spaces provided
Part A: Finding the Answer
In this section, you are going to use the formulas for linear functions (ax + by =c and y=mx + b)
For each question, answer the question giving the clues that you used in determining your answer. You will be given two
marks – one mark for your correct clues and one mark for the correct answer.
True/False
Indicate whether the statement is true or false.
_True___1. The slope of the equation y=5x+2 is 5 and the y-intercept is 2.
__False__ 2. The equation y= has a slope of 4 and a y-intercept of .
_True___3. The equation 2y=4x+8 has the slope of 2 and y-intercept of 4
__False__ 4.The equation y=4 produces a horizontal line through the x value of 4.
Page 1
Comparing with y = mx + c, m=5, c=2
Comparing with y = mx + c, m= -1/2, c= 4
Comparing with y = mx + c, m= 2, c= 4
The line does not pass through (4,0)

__True__5. The x intercept of the equation x+y=4 is 4.
_True___6. The y intercept of the equation -x+4y=8 is 2.
__False__ 7. The equation 2x+5y = 10 has the x intercept of 2 and a y intercept of 5.
Part B: Solving the Problems
In this section, you are going to use the formulas for linear functions (ax + by =c and y=mx + b)
For each question, answer the question giving the clues that you used in determining your answer. You will be given two
marks - three mark for your correct clues and one mark for the correct answer.
8. Given two points (5,2) and (-1,8) the slope is:
9. Given two points (3,7) and (-5,-9) the slope of the line is:
10. Solve for x. Round your answer to one decimal place.
6x+7=5
Page 2
(x/4) + (y/4)= 1
X int = 4
(x/-2) + (y/2)= 1
Y int : 2
(x/5) + (y/2)= 1
X int = 5 , y int = 2
Slope: 8−2
−1−5 = -1
Slope: −9−7
−5−3 = 2
X= (5-7)/6 = -1/3

11. Given the function with the slope of and the y intercept of-3, write the equation for
this function in standard form.
12. For the graph with the points of (3,4) and (-2 and 6)
a) determine the slope of the line
b) using one point for the x and y values, and the slope you find in part a, find the
value of b in the equation y=mx + b
13. In the equation y = mx + b, the value of m is the value of b is -3
Using these values, sketch the graph in the space provided.
Page 3
y− 3
4 x=−3
Slope = -2/5
( y−4 ) =−2
5 ( x−3 )
y=−2
5 x + 26
5 b = 26/5

14. If the value of m = 4 and b = -3:
a) write the equation in y=mx + b form
b) what is the x-intercept for this graph
c) what is the y-intercept for this graph
d) verify your calculations by making a graph on the paper provided.
Page 4
Y= 4x-3
X int = ¾
Y int = -3