unit 2 lesson 2 slope & equations of lines · •find the slope of a line from a graph •find...
TRANSCRIPT
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UNIT 2 LESSON 2
SLOPE & EQUATIONS OF LINES
COLLEGE PREP
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WARM UP
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OBJECTIVES
•Find the slope of a line from a graph
•Find the slope of a line given 2 points
•Graph a line that is in slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏)
•Write the equation of a line in slope-intercept form given
a graph or a set of two points
•Use the point-slope form of the equation to write the
equation of a line
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SLOPE-INTERCEPT FORM
Standard Form: A𝑥 + B𝑦 = C
If the standard form of a line is solved for 𝑦, a new form is created: slope-intercept form:
𝑦 = 𝑚𝑥 + 𝑏where 𝑚 is the slope and 𝑏 is the 𝑦-intercept.
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SLOPE-INTERCEPT FORM
Write the equation in slope-intercept form.
Identify the slope and the 𝑦-intercept.
A) 3𝑥 + 4𝑦 = 20
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SLOPE-INTERCEPT FORM
Write the equation in slope-intercept form.
Identify the slope and the 𝑦-intercept.
B) 5𝑥 − 𝑦 = 7
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SLOPE
Slope is the ratio of the change in 𝑦 to the change in 𝑥.
𝑅𝐼𝑆𝐸 (𝑦)
𝑅𝑈𝑁 (𝑥)=change in 𝑦
change in 𝑥=𝑦2 − 𝑦1𝑥2 − 𝑥1
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SLOPE
Use the given point and slope to find a second point on
the graph.
C) Point: (1, −3) D) Point: (−2,10)
Slope: 3
4Slope: −3
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SLOPE-INTERCEPT FORM
E) Graph 𝑦 = −2
3𝑥 + 2
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SLOPE-INTERCEPT FORM
F) Graph 𝑦 = 5𝑥 − 1
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SLOPE-INTERCEPT FORM
G) Graph 3𝑥 + 2𝑦 = −4
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SLOPE-INTERCEPT FORM
H) A 𝑦-intercept of 3 is shown at (0,3).Use this intercept to create the following:
Draw a line with a positive slope.Find the equation of that line.
Draw a line with a negative slope.Find the equation of that line.
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SLOPE-INTERCEPT FORM
I) Write the equation of the line shown.
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SLOPE-INTERCEPT FORM
Find the slope of the following graphs:
J) K)
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SLOPE-INTERCEPT FORM
Find the slope of the line that passes through the points:
L) 3,4 , (6, −8) M) 1,2 , (−3,−7)
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POINT-SLOPE FORM
Point-Slope form uses a point and the slope to create a
linear equation. Using a point (𝑥1, 𝑦1) and a slope 𝑚
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
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POINT-SLOPE FORM
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
N) What is the equation of the line that has a slope of 3
and goes through (3,5)?
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POINT-SLOPE FORM
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)
O) What is the equation of the line that has a slope of −2and goes through (−1,2)?
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POINT-SLOPE FORM
P) What is the equation of the line that goes through
−2,3 and (1, −1)?
HINT: What do today’s two formulas for a line have in
common?
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POINT-SLOPE FORM
Q) Find a linear function 𝑓 such that 𝑓 2 = 7 and
𝑓 3 = 4. What is 𝑓(5).
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OBJECTIVES
•Find the slope of a line from a graph
•Find the slope of a line given 2 points
•Graph a line that is in slope-intercept form (𝑦 = 𝑚𝑥 + 𝑏)
•Write the equation of a line in slope-intercept form given
a graph or a set of two points
•Use the point-slope form of the equation to write the
equation of a line
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HOMEWORK
In Class Assignment 2.2
Homework 2.2
EDPuzzle 2.2