Connecting Algebra 1 to Advanced Placement* Mathematics
A Resource and Strategy Guide
Write the Equation of the Line – Review
Objective:
Students will be assessed on their ability to write the equation of a line in multiple methods.
Connections to Previous Learning:
Students should be able to write the equation of a line using a graph, slope – intercept, two points,
point-slope.
Connections to AP*:
AP Calculus Topic: Analysis of Functions
Materials:
Student Activity pages
Teacher Notes:
This lesson can be used as a review or as an assessment.
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Student Activity
Write the Equation of the Line – Review
1.
Use the graph showing line b below to answer the following. Be sure to show the steps which
justify EACH part of each answer. Your work will be graded based on the explanations that
you give, not just based on your answer.
a)
What is the slope of this line? Explain how you got this answer two different ways.
b)
What is the y-intercept of this line?
c)
Explain how to use the graph to write an equation for this line in slope-intercept form.
Give the equation of the line.
d)
Choose any two points on the graph and explain how to find the equation in slopeintercept form from those two points.
e)
Choose any point on the graph and the slope that you determined in part a. Write an
equation in point-slope form for this line.
f)
Re-write your equation from part e in standard form.
g)
Re-write your equation from part e in slope-intercept form.
h)
If line b is shifted down 3 units, what is the equation of the new line?
i)
If line b is shifted to the right 4 units, what is the equation of the new line?
line b
10
-10 -8 -6 -4 -2
10
8
8
6
6
4
4
2
2
-2
2
4
6
8 10
-10 -8 -6 -4 -2
-2
-4
-4
-6
-6
-8
-8
-10
-10
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2
4
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Student Activity
2.
Use the points (3, 0) and (0, -2) to answer the following. (You may use the grid above to graph
the points if you wish.)
a)
What is the slope of the line which passes through these two points?
b)
Write the equation of the line passing through these points. Use slope-intercept form.
c)
Write the equation of the line passing through these points. Use point-slope form.
d)
Write the equation of the line passing through these points in standard form.
e)
Write the equation of any line which is perpendicular to this line.
f)
Write the equation of a line which is parallel to this line which passes through the point
(1, 3). Give your answer in standard form.
®
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Connecting Algebra 1 to Advanced Placement* Mathematics
A Resource and Strategy Guide
Write the Equation of the Line – Review
Answers:
1. a) One way is to just count on the coordinate plane. The rise is 2 and the run is 1, so the slope
is 2. Another way is to pick any two points on the line. I’ll use (0, -1) and (1, 1). The slope
1 − ( −1) 2
is
= = 2.
1− 0
1
b) The y-intercept, from looking at where the graph crosses the y-axis, is –1.
c) From the graph I counted the slope and found that it is 2, see part a. Then I found that the yintercept is –1, see part b. Since the equation of the line in slope-intercept form is
y = mx + b, the equation of this line is y = 2x – 1
3 −1
= 2.
2 −1
Next use this slope and one ordered pair. I’ll use (1, 1). 1 = 2(2) + b. Solving this equation
for b, I get b = –1. Substituting for the slope and y-intercept, the equation is
y = 2x – 1.
d) I’ll use the points (1, 1) and (2, 3). From these points, find the slope which is
e) I’ll use (1, 1) and the slope is 2, so y – 1 = 2(x – 1).
f) Re-write your equation from part e in standard form.
after adding –2x and 1 to both sides
y – 1 = 2(x – 1)
y – 1 = 2x – 2
-1(y – 2x = -1)
2x – y = 1
g) Re-write your equation from part e in slope-intercept form. y – 1 = 2(x – 1)
y – 1 = 2x – 2
after adding 1 to each side y = 2x – 1
h) Since the original equation is y = 2x – 1, a shift down 3 units will take the y-intercept down 3
from -1. Since -1 + -3 is -4, the new y-intercept is –4, and the new equation is
y = 2x – 4.
i
From looking at the graph, I see that the point (-4, -9) would move to the y-axis. This
would make the new y-intercept (0, -9). The new equation would be y = 2x – 9, or
y = 2(x – 4 ) – 1 = 2x – 9.
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Answers
2. a) The slope is
−2−0 −2 2
=
= .
0−3
−3 3
2
x – 2. I know the
3
y-intercept because it is the y-coordinate when x is zero, and we were given that point.
b) The equation of the line passing through these points is y =
c) Since we found the slope in part (a), and using (3, 0), the equation is y – 0 =
2
(x – 3).
3
d) Since the two points given were the intercepts, the equation can be found by just working
backwards. The equation is 2x – 3y = 6 since 2 times 3 is 6 and
–3 times –2 is 6 or 3y = 2x – 6.
e) The equation of a line perpendicular to this line has to have a slope of −
possible equation would be of the form y = −
3
x + b.
2
f) A line parallel to this line will have the same slope,
Using point-slope form,
clearing fractions and parentheses
subtracting 3y and -2 from each side
The equation in standard form is
®
3
, so in general, a
2
2
.
3
2
(x – 1)
3
3y – 9 = 2x – 2
–7 = 2x – 3y.
2x – 3y = –7.
y–3=
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