Lesson Menu 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

Main Idea/Vocabulary Find the slope of a line. slope rise run

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.

Example 1 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.

Example 1 CYP SKATEBOARDING A skateboard hill falls 10 inches for every horizontal change of 14 inches. What is the slope of the hill? A. B. C. D.

Example 2 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

Example 2 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 –

Example 2 CYP 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

Example 3 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.

Example 3 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

Example 3 CYP 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.

Key Concept 4

Example 4 Find the slope of the line that passes through A(3, 3) and B(2, 0). Find Slope Using Coordinates Slope formula (x 1, y 1 ) = (3, 3) (x 2, y 2 ) = (2, 0) Simplify. or 3

Example 4 CheckWhen 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.

Example 4 CYP Find the slope of the line that passes through L(4, –1) and M(0, 5). A. B.–1 C. D.

Example 5 Find Slope Using Coordinates Find the slope of the line that passes through X(−2, 3) and Y(3, 0). Slope formula (x 1, y 1 ) = (–2, 3) (x 2, y 2 ) = (3, 0) Simplify.

Example 5 CheckWhen 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

Example 5 CYP 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). Five Minute Check 1 A. B. C. D.

Find the slope of the line that passes through M(–3, 2) and N(7, –5). Five Minute Check 2 A. B. C. D.

Find the slope of the line that passes through P(–6, –9) and Q(2, 7). Five Minute Check 3 A.–2 B. C. D.2

Find the slope of the line that passes through K(6, –3) and L(16, –4). Five Minute Check 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.) Five Minute Check 5 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? Five Minute Check 6 A.3 B. C. D.−3