lesson menu main idea and new vocabulary ngsss example 1:real-world example example 2:find slope...

Main Idea and New Vocabulary

NGSSS

Example 1: Real-World Example

Example 2: Find Slope Using a Graph or Table

Example 3: Find Slope Using a Graph or Table

Key Concept: Slope Formula

Example 4: Find Slope Using Coordinates

Example 5: Find Slope Using Coordinates

Five-Minute Check

• Find the slope of a line.

• slope

• rise

• run

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

ACCESS RAMPS The access ramp from the sidewalk to the door of a hotel rises 8 inches for every horizontal change of 96 inches. What is the slope of the access ramp?

Definition of slope

rise = 8 in., run = 96 in.

Simplify.

Answer: The slope of the ramp is .

SKATEBOARDING A skateboard hill falls 10 inchesfor every horizontal change of 14 inches. What isthe slope of the hill?

A.

B.

C.

D.

PHOTOGRAPHY The graph shows the position of a photograph leaning against a wall. Find the slope of the line.

Find Slope Using a Graph or Table

Choose two points on the line. The vertical change is –3 units and the horizontal change is 1 unit.

Definition of slope

Find Slope Using a Graph or Table

rise = –3, run = 1

Answer: The slope of the line is or –3.

or –

ELEPHANTS The graph shows the bales of hay that an elephant at a zoo eats each week. Find the slope of the line.

A. 1

B.

C. 30

D. 40

Find Slope Using a Graph or Table

PAINTING The table shows the number of gallons of paint Mrs. Brown used to paint the number of rooms. Find the slope of the line. Then graph it.

Choose two points from the table to find the changes in the x- and y-values.

Find Slope Using a Graph or Table

Answer: The slope is .

Definition of slope

HUMMINGBIRDS The table shows the number of hummingbird feeders and the amount of nectar used to fill the feeders. Find the slope of the line. Then graph it.

A. C.

B. D.

Find the slope of the line that passes through A(3, 3) and B(2, 0).

Find Slope Using Coordinates

Slope formula

(x1, y1) = (3, 3)

(x2, y2) = (2, 0)

Simplify.or 3

Check When going from left to right, the graph of the line slants upward. This is correct for positive slope.

Find Slope Using Coordinates

Answer: The slope is 3.

Find the slope of the line that passes through L(4, –1) and M(0, 5).

A.

B. –1

C.

D.

Find Slope Using Coordinates

Find the slope of the line that passes through X(−2, 3) and Y(3, 0).

Slope formula

(x1, y1) = (–2, 3)

(x2, y2) = (3, 0)

Simplify.

Check When going from left to right, the graph of the line slants downward. This is correct for negative slope.

Find Slope Using Coordinates

Answer: The slope is

Find the slope of the line that passes through R(1, 8) and S(–2, 2).

A. –2

B.

C.

D. 2

Find the slope of the line that passes through A(0, 0) and B(4, 3).

A.

B.

C.

D.

Find the slope of the line that passes through M(–3, 2) and N(7, –5).

A.

B.

C.

D.

Find the slope of the line that passes through P(–6, –9) and Q(2, 7).

A. –2

B.

C.

D. 2

Find the slope of the line that passes throughK(6, –3) and L(16, –4).

A. –10

B.

C.

D. 10

Do the following points form a parallelogram when they are connected? Explain. A(5, 4), B(10, 4), C(5, −1), D(0, 0)(Hint: Two lines that are parallel have the same slope.)

A. Yes; the slopes of and are equal.

B. Yes; the slopes of and are equal.

C. Yes; the slopes of the opposite sides are equal.

D. No; the slope of is 0, but the slope of

is

What is the slope of the graph?

A. 3

B.

C.

D. −3