Objective: In this lesson you will see how the constant b affects the line graph.
1. Use a graphing calculator to graph each equation and complete the following
chart. An example is solved for you.
|y = x – 3||1||-3||(0,-3)||(3,0)|
|y = x + 4|
|y = x + 5.5|
|y = 2x – 5|
|y = 2x + 4.8|
|y = 3x – 2|
|y = -3x + 7|
|y = -3x|
2. Use the results to answer the following questions.
a. If b has a positive value, then the y-intercept is (above, below) the x-axis. Circle one answer.
b. If b has a negative value, then the y-intercept is (above, below) the x-axis. Circle one answer.
c. What is the y-intercept of the equation y = 2x + 4? _________________________
d. What is the y-intercept of the equation y = mx + b? ________________________
3. Answer the following questions about the first three entries in Exercise 1.
a. What is the same about all three graphs? ________________________________
b. These lines never intersect so we say they are ___________________________
c. What is the relationship between b and the x-intercept in these equations?
d. What are the x- and y-intercepts of y = x – 5? ____________________________
e. How does changing the value of b affect graphs of the form y = x + b? _________
4. Describe and compare the graphs of y = 3x – 1 and y = 3x + 2. (Use a graphing
calculator to help you see the graphs.) __________________________________
5. Write an equation whose graph is a horizontal line. ________________________
6. Write an equation whose graph is a horizontal line through (0, 2.5). ____________
7. Write an equation whose graph is a line parallel to and between the graphs of
y = 3x + 2 and y = 3x + 4.5 ____________________________________________
8. Write and equation whose graph is a line parallel to the graph of y = -3x +
1, but with
y-intercept (0,-5). ____________________________________________________
Objective: In this lesson you will see how to graph equations that are not in
slope-intercept form y = mx + b.
Solve each equation for y then write the equation in slope-intercept form. Find
slope, and x- and y-intercepts, and graph the line. An example is solved.
|2x + y – 3 = 0
Solve for y:
|Y = -2x + 3
Slope = -2
x-intercept = (1.5,0)
|Y + 3x = 4|
|Y – 3.5 = 2x|
|5x – y = 15|
|-1x = 4 + y|
|2y + 5x – 7 = 0|
Write your own problem below. Follow the directions above to solve and graph the
Objective: In this lesson you will see how to find the equation of a line by
at its graph.
Examine each graph below and predict its equation. Then use the graphing
to test your prediction. The first problem is solved for you.
The y-intercept is (0, 3). ----->" b = 3
The slope is positive and equals 1. ---->" m = 1
The slope-intercept form ----->" y = mx + b
Substitute the values of m and b.
y = 1x +3
Equation: y = x + 3