4.1 Graphing Equations in Slope Intercept Form

Algebra 1

Content Standards

F.IF.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.

S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Mathematical Practices

2 Reason abstractly and quantitatively.

8 Look for and express regularity in repeated reasoning.

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

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.

B for BEGIN….M for

MOVE!!!

Example 1Write 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 1B

Step 1: Plot the y-intercept

Step 2: The slope is

From (0, –1), move up 1 unit and right 4 units. Plot the point.

Step 3: Draw a line through the points.

You Try!

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 2Graph 5x + 4y = 8.Solve for y to write the equation in slope-intercept form.

Example 2BSlope-intercept form

Step 1: Plot the y-intercept

Now graph the equation.

From (0, 2), move down 5 units and right 4 units. Draw a dot.

Step 2: The slope is

Step 3: Draw a line connecting the points.

You Try!Graph 2x + y = 6.

Step 1:

Step 2:

Step 3:

Example 3Graph y = –7.

Step 1 Plot the y-intercept:

Step 2 The slope is 0. Draw a line through the points with the y-coordinate 7.

Does your graph look like this?!

Reminder: Think of Mr. Slope Guy!

You Try!Graph 5y = 10.

A. B.

C. D.

Example 4Which of the following is an equation in slope-intercept form for the line shown in the graph?

A.

B.

C.

D.

You Try!Which of the following is an equation in slope-intercept form for the line shown in the graph?

A.

B.

C.

D.

Example 5: ApplicationHEALTH 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 5B Write and Graph a Linear Equation

B. Graph the equation.

Answer:

The graph passes through (0, 117) with a slope of

Example 5C 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.

You Try!

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 D spent for any year n since 1986.

You Try!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.

You Try!

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.

End of the LessonHomework: 4.1 Practice Worksheet (ALL)