Splash Screen Graphing Equations in Slope-intercept Form Lesson 4-1.

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Presentation transcript:

Splash Screen Graphing Equations in Slope-intercept Form Lesson 4-1

Over Chapter 3

Then/Now You found rates of change and slopes. Write and graph linear equations in slope-intercept from. Model real-world data with equations in slope-intercept form.

Concept Slope-intercept form of a line

Example 1 Write and Graph an Equation Write an equation in slope-intercept form of the line with a slope of and a y-intercept of –1. Then graph the equation. Slope-intercept form

Now graph the equation. Example 1 Write and Graph an Equation Step 1Plot the y-intercept (0, –1). Step 2The slope is. From (0, –1), move up 1 unit and right 4 units. Plot the point. Step 3Draw a line through the points. Answer:

Example 1 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.

Example 2 Graph Linear Equations Graph 5x + 4y = 8. **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

Example 2 Graph Linear Equations Slope-intercept form Step 1Plot the y-intercept (0, 2). Now graph the equation. From (0, 2), move down 5 units and right 4 units. Draw a dot. Step 2Use the slope, to find the next point Step 3Draw a line connecting the points. Answer:

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

Example 3 Graph Linear Equations Graph y = –7. Step 1Plot the y-intercept (0,  7). Step 2The slope is 0. Draw a line through the points with the y-coordinate  7. Answer:

Example 3 Graph 5y = 10. A.B. C.D.

Example 4 Which of the following is an equation in slope-intercept form for the line shown in the graph? A. B. C. D.

Example 4 Read the Test Item You need to find the slope and y-intercept of the line to write the equation. Step 1The line crosses the y-axis at (0, –3), so the y-intercept is –3. The answer is either B or D. Solve the Test Item

Example 4 Step 2To get from (0, –3) to (1, –1), go up 2 units and 1 unit to the right. The slope is 2. Step 3Write the equation. y = mx + b y = 2x – 3 Answer: The answer is B.

Example 4 Which of the following is an equation in slope- intercept form for the line shown in the graph? A. B. C. D.

Example 5 Write and Graph a Linear Equation HEALTH The ideal maximum heart rate for a 25-year-old exercising to burn fat is 117 beats per minute. For every 5 years older than 25, that ideal rate drops 3 beats per minute. A. Write a linear equation to find the ideal maximum heart rate for anyone over 25 who is exercising to burn fat.

Example 5 Write and Graph a Linear Equation

Example 5 Write and Graph a Linear Equation B. Graph the equation. Answer: The graph passes through (0, 117) with a slope of

Example 5 Write and Graph a Linear Equation C. Find the ideal maximum heart rate for a 55-year-old person exercising to burn fat. Answer:The ideal maximum heart rate for a 55-year- old person is 99 beats per minute. The age 55 is 30 years older than 25. So, a = 30. Ideal heart rate equation Replace a with 30. Simplify.

Example 5 A.D = 0.15n B.D = 0.15n + 3 C.D = 3n D.D = 3n A. The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since Consumers spent $3 million in Write a linear equation to find the average amount D spent for any year n since 1986.

Example 5 B. The amount of money spent on Christmas gifts has increased by an average of $150,000 ($0.15 million) per year since Consumers spent $3 million in Graph the equation. A.B. C.D.

Example 5 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 Consumers spent $3 million in Find the amount spent by consumers in 1999.

End of the Lesson Homework Page 221 #17 – 59 odd