lesson 3 mi/vocab
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• slope-intercept form
• Write and graph linear equations in slope-intercept form.
• Model real-world data with an equation in slope-intercept form.
BrainPOP:Slope and Intercept
Slope-intercept form
Answer:
Write an equation in slope-intercept form of the line
whose slope is and whose y-intercept is –6.
Write an Equation Given Slope and y-Intercept
A. AB. BC. CD. D
A B C D
0% 0%0%0%
A. y = 3x + 4
B. y = 4x + 3
C. y = 4x
D. y = 4
Write an equation in slope-intercept form of the line whose slope is 4 and whose y-intercept is 3.
Write an Equation From a Graph
Write an equation in slope-intercept form of the line shown in the graph.
Step 1 You know the coordinates of two points on the line. Find the slope. Let (x1, y1) = (0, –3) and (x2, y2) = (2, 1).
(x1, y1) = (0, –3)
(x2, y2) = (2, 1)
Write an Equation From a Graph
Simplify.
Answer: The equation of the lines is y = 2x – 3.
The slope is 2.
Step 2 The line crosses the y-axis at (0, –3).So, the y-intercept is –3.
Step 3 Finally, write the equation.
Slope-intercept form
Simplify.
y = mx + b
y = 2x – 3
1. A2. B3. C4. D
0%0%0%0%
A B C D
Write an equation in slope intercept form of the line shown in the graph.
A.
B.
C.
D.
Graph Equations
A. Graph y = 0.5x – 7.Step 1 The y-intercept is –7.
So graph (0, –7).
From (0, –7), move up 1 unit and right 2 units. Draw a dot.
Step 3 Draw a line through the points.
Step 2 The slope is 0.5
Graph Equations
B. Graph 5x + 4y = 8.Step 1 Solve for y to write the equation in slope-
intercept form.
8 – 5x = 8 + (–5x) or –5x + 8
Subtract 5x from each side.
Simplify.
Original equation
Divide each side by 4.
5x + 4y = 8
5x + 4y – 5x = 8 – 5x
4y = 8 – 5x
4y = –5x + 8
Graph Equations
Divide each term in the numerator by 4.
Step 2 The y-intercept of
So graph (0, 2).
Graph Equations
From (0, 2), move down 5 units and right 4 units. Draw a dot.
Step 3 The slope is
Step 4 Draw a line connecting the points.
Answer:
A. HEALTH The ideal maximum heart rate for a 25-year-old who is exercising to burn fat is 117 beats per minute. For every 5 years older than 25, that ideal rate drops 3 beats per minute. Write a linear equation to find the ideal maximum heart rate for anyone over 25 who is exercising to burn fat.
Write an Equation in Slope-Intercept Form
Answer:
Write an Equation in Slope-Intercept Form
Words
Variables
Equation
Let R = the ideal heart rate.
Let a = years older than 25.
ideal rateIdeal rate of years older for 25- rate equals change times than 25 plus year-old.
R = × a + 117
B. Graph the equation.
Answer:
Write an Equation in Slope-Intercept Form
The graph passes through (0, 117) with a slope of
C. Find the ideal maximum heart rate for a person exercising to burn fat who is 55 years old.
Answer: The ideal heart rate for a 55-year-old person is 99 beats per minute.
Write an Equation in Slope-Intercept Form
The age 55 is 30 years older than 25. So, a = 30.
Ideal heart rate equation
Replace a with 30.
Simplify.
A. AB. BC. CD. D
A B C D
0% 0%0%0%
A. D = 0.15n
B. D = 0.15n + 3
C. D = 3n
D. D = 3n + 0.15
A. The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. Write a linear equation to find the average amount spent for any year since 1986.
A. AB. BC. CD. D
A B C D
0% 0%0%0%
B. The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. Graph the equation.
A.B.
C.D.
A. AB. BC. CD. D
A B C D
0% 0%0%0%
A. $5 million
B. $3 million
C. $4.95 million
D. $3.5 million
C. The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since 1986. Consumers spent $3 million in 1986. Find the amount spent by consumers in 1999.
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