Write and graph linear equations in slope-intercept form.

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Write and graph linear equations in slope-intercept form. Model real-world data with an equation in slope-intercept form. slope-intercept form Lesson 3 MI/Vocab

BrainPOP: Slope and Intercept Lesson 3 Key Concept 1

Write an Equation Given Slope and y-Intercept Write an equation in slope-intercept form of the line whose slope is and whose y-intercept is –6. Slope-intercept form Answer: Lesson 3 Ex1

Write an equation in slope-intercept form of the line whose slope is 4 and whose y-intercept is 3. A. y = 3x + 4 B. y = 4x + 3 C. y = 4x D. y = 4 A B C D Lesson 3 CYP1

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) Lesson 3 Ex2

Write an Equation From a Graph Simplify. 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. y = mx + b Slope-intercept form y = 2x – 3 Simplify. Answer: The equation of the lines is y = 2x – 3. Lesson 3 Ex2

Write an equation in slope intercept form of the line shown in the graph. B. C. D. A B C D Lesson 3 CYP2

Step 1 The y-intercept is –7. So graph (0, –7). Graph Equations A. Graph y = 0.5x – 7. Step 1 The y-intercept is –7. So graph (0, –7). Step 2 The slope is 0.5 From (0, –7), move up 1 unit and right 2 units. Draw a dot. Step 3 Draw a line through the points. Lesson 3 Ex3

Step 1 Solve for y to write the equation in slope-intercept form. Graph Equations B. Graph 5x + 4y = 8. Step 1 Solve for y to write the equation in slope-intercept form. 5x + 4y = 8 Original equation 5x + 4y – 5x = 8 – 5x Subtract 5x from each side. 4y = 8 – 5x Simplify. 4y = –5x + 8 8 – 5x = 8 + (–5x) or –5x + 8 Divide each side by 4. Lesson 3 Ex3

Divide each term in the numerator by 4. Graph Equations Divide each term in the numerator by 4. Step 2 The y-intercept of So graph (0, 2). Lesson 3 Ex3

From (0, 2), move down 5 units and right 4 units. Draw a dot. Graph Equations Step 3 The slope is From (0, 2), move down 5 units and right 4 units. Draw a dot. Step 4 Draw a line connecting the points. Answer: Lesson 3 Ex3

A. Graph y = 2x – 4. A. B. C. D. A B C D Lesson 3 CYP3

B. Graph 3x + 2y = 6. A. B. C. D. A B C D Lesson 3 CYP3

Write an Equation in Slope-Intercept Form 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. Lesson 3 Ex4

Write an Equation in Slope-Intercept Form ideal rate Ideal rate of years older for 25- rate equals change times than 25 plus year-old. Words Variables Equation Let R = the ideal heart rate. Let a = years older than 25. R = × a + 117 Answer: Lesson 3 Ex4

Write an Equation in Slope-Intercept Form B. Graph the equation. The graph passes through (0, 117) with a slope of Answer: Lesson 3 Ex4

Write an Equation in Slope-Intercept Form C. Find the ideal maximum heart rate for a person exercising to burn fat who is 55 years old. The age 55 is 30 years older than 25. So, a = 30. Ideal heart rate equation Replace a with 30. Simplify. Answer: The ideal heart rate for a 55-year-old person is 99 beats per minute. Lesson 3 Ex4

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. D = 0.15n B. D = 0.15n + 3 C. D = 3n D. D = 3n + 0.15 A B C D Lesson 3 CYP4

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 B C D Lesson 3 CYP4

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. A. $5 million B. $3 million C. $4.95 million D. $3.5 million A B C D Lesson 3 CYP4