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Investigating Liner Equations Using Graphing CalculatorActivity 2

Equation  Value of m 
Value of b 
Sketch  yintercept  xintercept 
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 yintercept is (above, below) the xaxis.
Circle one answer.
b. If b has a negative value, then the yintercept is (above, below) the xaxis.
Circle one answer.
c. What is the yintercept of the equation y = 2x + 4? _________________________
d. What is the yintercept 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 xintercept in these equations?
____________________________________________________________________
d. What are the x and yintercepts 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
yintercept (0,5). ____________________________________________________
Objective: In this lesson you will see how to graph equations that are not in
the
slopeintercept form y = mx + b.
Solve each equation for y then write the equation in slopeintercept form. Find
the
slope, and x and yintercepts, and graph the line. An example is solved.
Equation  Equation in slopeintercept form 
sketch 
2x + y – 3 = 0 Solve for y: 
Y = 2x + 3 Slope = 2 yintercept =(0,3) xintercept = (1.5,0) 

Y + 3x = 4  
Y – 3.5 = 2x  
5x – y = 15  
1x = 4 + y  
2y + 5x – 7 = 0  
Challenge: Write your own problem below. Follow the directions above to solve and graph the line. 

Objective: In this lesson you will see how to find the equation of a line by
looking
at its graph.
Examine each graph below and predict its equation. Then use the graphing
calculator
to test your prediction. The first problem is solved for you.
Reasoning: The yintercept is (0, 3). >" b = 3 The slope is positive and equals 1. >" m = 1 The slopeintercept form >" y = mx + b Substitute the values of m and b. y = 1x +3 Equation: y = x + 3 
