Main Idea and New Vocabulary

Example 1: Find Slopes and y-intercepts

Example 2: Find Slopes and y-intercepts

Example 3: Write an Equation in Slope-Intercept Form

Example 4: Write an Equation in Slope-Intercept Form

Example 5: Graph Using Slope-Intercept Form

Example 6: Graph an Equation to Solve Problems

Example 7: Graph an Equation to Solve Problems

• Graph linear equations using the slope and y-intercept.

• slope-intercept form

• y-intercept

Find Slopes and y-intercepts

State the slope and y-intercept of the graph of

y = x – 5.

Write the equation in the form y = mx + b.

Answer: The slope of the graph is , and the

y-intercept is −5.

State the slope and y-intercept of the graph of

.

A. slope: ; y-intercept: 1

B. slope: ; y-intercept: 1

C. slope: 1; y-intercept:

D. slope: 1; y-intercept:

State the slope and y-intercept of the graph of 2x + y = 8.

Find Slopes and y-intercepts

2x + y = 8 Write the original equation.

2x – 2x + y= 8 – 2x Subtract 2x from each side.

y = 8 − 2x Simplify.

y= −2x + 8 Write the equation in the form y = mx + b.

y = mx + b m = –2, b = 8

Answer: The slope of the graph is –2 and the y-intercept is 8.

A. slope: –4; y-intercept: 10

B. slope: 4; y-intercept: 10

C. slope: 10; y-intercept: –4

D. slope: 10; y-intercept: 4

State the slope and y-intercept of the graph of y – 4x = 10.

Write an Equation in Slope-Intercept Form

Write an equation of a line in slope-intercept form with a slope of 2 and a y-intercept of –8.

y= mx + b Slope-intercept form

y= 2x + (–8) Replace m with 2 and b with –8.

y= 2x – 8Simplify.

Answer: y = 2x – 8

A. y = – x – 6

B. y = – x + 6

C. y = x + 6

D. y = 6x –

Write an equation of a line in slope-intercept

form with a slope of – and a y-intercept of 6.

Write an equation in slope-intercept form for the graph shown.

Write an Equation in Slope-Intercept Form

The y-intercept is 1. From (0, 1), you move up 2 units and left 3 units to another point on the line.

So, the slope is – .

Write an Equation in Slope-Intercept Form

y = mx + b Slope-intercept form

y = – x + 1

Answer: y = – x + 1

y = – x + 1 Replace m with – and b with 1.

Write an equation in slope-intercept form for the graph shown.

A. y = –3x – 2

B. y = 3x – 2

C. y = – x – 1

D. y = x – 1

Graph Using Slope-Intercept Form

Step 1 Find the slope and y-intercept.

Graph using the slope and

y-intercept.

y = x + 2 slope = , y-intercept = 2

Graph Using Slope-Intercept Form

Step 2 Graph the y-intercept 2.

Graph Using Slope-Intercept Form

Step 3 Use the slope to locate a second point on the line.

←change in y: up 2 units←change in x: right 3 unitsm =

Graph Using Slope-Intercept Form

Answer:

Step 4 Draw a line through the two points.

Graph y = – x + 3 using the slope and y-intercept.

A. B.

C. D.

KAYAK RENTAL A kayak rental pavilion charges $15.00 per hour and $2.50 for instruction on how to not fall out of the kayak. The total cost is given by the equation y = 15x + 2.5, where x is the number of hours the kayak is rented. Graph the equation to find the total cost for 2 hours.

y = 15x + 2.5 slope = 15, y-intercept = 2.5

Graph an Equation to Solve Problems

Plot the point (0, 2.5).

Locate another point up 15 and right 1.

Draw the line.

The y-coordinate is 32.5 when the x-coordinate is 2, so the total cost for 2 hours is $32.50.

Graph an Equation to Solve Problems

Answer: The total cost for 2 hours is $32.50.

A. $26

B. $80

C. $90

D. $100

POTTERY A pottery studio charges $16 per hour and $10 for firing fees. The total cost is given by the equation y = 16x + 10, where x is the number of hours a customer uses the studio. Graph the equation to find the total cost for 5 hours.

KAYAK RENTAL A kayak rental pavilion charges $15.00 per hour and $2.50 for instruction on how to not fall out of the kayak. The total cost is given by the equation y = 15x + 2.5, where x is the number of hours the kayak is rented. Interpret the slope and the y-intercept.

Graph an Equation to Solve Problems

Graph an Equation to Solve Problems

Answer: The slope 15 represents the rate of change or cost per hour. The y-intercept 2.5 is

the charge for instruction.

A. The slope 10 represents the firing fee. The y-intercept 16 is the cost per hour.

B. The slope 10 represents the cost per hour. The y-intercept 16 is the firing fee.

C. The slope 16 represents the firing fee. The y-intercept 10 is the cost per hour.

D. The slope 16 represents the cost per hour. The y-intercept 10 is the firing fee.

POTTERY A pottery studio charges $16 per hour and $10 for firing fees. The total cost is given by the equation y = 16x + 10, where x is the number of hours a customer uses the studio. Interpret the slope and the y-intercept.