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Lesson Menu. Main Idea and New Vocabulary NGSSS 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

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Lesson menu

Lesson Menu

Main Idea and New Vocabulary

NGSSS

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

Five-Minute Check


Main idea vocabulary

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

  • slope-intercept form

  • y-intercept

Main Idea/Vocabulary


Ngsss

MA.8.A.1.2 Interpret the slope and the x- and y-intercepts when graphing a linear equation for a real-world problem.

NGSSS


Example 1

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.

Find Slopes and y-intercepts

Example 1


Example 1 cyp

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:

Example 1 CYP


Example 2

Find Slopes and y-intercepts

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

2x + y= 8 Write the original equation.

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

y= 8 − 2x Simplify.

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

y= mx + bm = –2, b = 8

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

Example 2


Example 2 cyp

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

A.slope: –4; y-intercept: 10

B.slope: 4; y-intercept: 10

C.slope: 10; y-intercept: –4

D.slope: 10; y-intercept: 4

Example 2 CYP


Example 3

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 + bSlope-intercept form

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

y= 2x – 8Simplify.

Answer: y = 2x – 8

Example 3


Example 3 cyp

Write an equation of a line in slope-intercept form with a slope of – and a y-intercept of 6.

A.y = – x – 6

B.y = – x + 6

C.y = x + 6

D.y = 6x –

Example 3 CYP


Example 4

So, the slope is – .

Write an Equation in Slope-Intercept Form

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

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

Example 4


Example 41

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

y = – x + 1

Answer: y = – x + 1

Write an Equation in Slope-Intercept Form

y = mx + bSlope-intercept form

Example 4


Example 4 cyp

A.y = –3x – 2

B.y = 3x – 2

C.y = – x – 1

D.y = x – 1

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

Example 4 CYP


Example 5

Graph using the slope and y-intercept.

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

Graph Using Slope-Intercept Form

Step 1Find the slope and y-intercept.

Example 5


Example 51

Graph Using Slope-Intercept Form

Step 2Graph the y-intercept 2.

Example 5


Example 52

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

m =

Graph Using Slope-Intercept Form

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

Example 5


Example 53

Graph Using Slope-Intercept Form

Step 4Draw a line through the two points.

Answer:

Example 5


Example 5 cyp

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

A.B.

C.D.

Example 5 CYP


Example 6

Graph an Equation to Solve Problems

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 + 2.5slope = 15, y-intercept = 2.5

Example 6


Example 61

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.

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

Example 6


Example 6 cyp

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.

A.$26

B.$80

C.$90

D.$100

Example 6 CYP


Example 7

Graph an Equation to Solve Problems

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.

Example 7


Example 71

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.

Example 7


Example 7 cyp

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.

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.

Example 7 CYP


Five minute check 1

A.m = ; b = 1

B.m = 1; b = 2

C.m = 2; b = –

D.m = 2; b = 1

State the slope and the y-intercept for the graph of the equation y = 2x + 1.

Five Minute Check 1


Five minute check 2

State the slope and the y-intercept for the graph of the equation y = 3x + 2.

A.m = –2; b = 3

B.m = 2; b = 3

C.m = 3; b = –2

D.m = 3; b = 2

Five Minute Check 2


Five minute check 3

State the slope and the y-intercept for the graph of the equation y = −2x + 4.5.

A.m = −4.5; b = –2

B.m = −2; b = 4.5

C.m = 2; b = 4.5

D.m = 4.5; b = –2

Five Minute Check 3


Five minute check 4

State the slope and the y-intercept for the graph of the equation 3x − y = 4.

A.m = 3; b = −4

B.m = –3; b = −4

C.m = 3; b = 4

D.m = −4; b = 3

Five Minute Check 4


Five minute check 5

The total price of apples y at an orchard can be calculated with the equation 1.12x + 5 = y, where x is the number of pounds of apples picked. What does the slope represent?

A.the total price of apples

B.the price of apples per pound

C.the number of apples per pound

D.the number of pounds of apples picked

Five Minute Check 5


Five minute check 6

A.y = 2x –

B.y = x + 2

C.y = x − 2

D.y = x – 2

What is the equation of the graph?

Five Minute Check 6


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