Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies...

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Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = – 5 when x = 10. Which is a direct variation equation that relates x and y? Find the next two terms in the arithmetic sequence –7, –4, –1, 2, …. Is the function represented by the table linear? Explain.

Transcript of Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies...

Page 1: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Warm ups

What is the slope of the line that passes through (–4, 8) and (5, 2)?

Suppose y varies directly as x and y = –5 when x = 10. Which is a direct variation equation that relates x and y?

Find the next two terms in the arithmetic sequence –7, –4, –1, 2, ….

Is the function represented by the table linear? Explain.

Page 2: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

4-1 GRAPHING IN SLOPE INTERCEPT FORMObjective: Write and graph linear equations in

slope-intercept from.

Page 3: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Vocabulary

• slope-intercept form y = mx + b

Page 4: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Slope-Intercept Form

Page 5: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

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

Page 6: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Now graph the equation .

Example 1 Graph

Write and Graph an Equation

Step 1 Plot the y-intercept (0, –1).

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.

Answer:

Page 7: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Try with a Mathlete

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.

Page 8: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

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

Page 9: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Example 2 Graph

Graph Linear Equations

Slope-intercept form

Step 1 Plot the y-intercept (0, 2).

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.

Answer:

Page 10: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Try with a MathleteGraph 3x + 2y = 6.

A.B.

C.D.

Page 11: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Example 3

Graph Linear Equations

Graph y = –7.

Step 1 Plot the y-intercept (0, -7).

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

Answer:

Page 12: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

TOOGraph 5y = 10.

A. B.

C. D.

Page 13: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

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

A.

B.

C.

D.

Page 14: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

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

A.

B.

C.

D.

Page 15: Warm ups What is the slope of the line that passes through (–4, 8) and (5, 2)? Suppose y varies directly as x and y = –5 when x = 10. Which is a direct.

Homework


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