Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–6) Then/Now New Vocabulary Key Concept: Slope-Intercept Form Example 1:Find the Slope and.

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Presentation transcript:

Splash Screen

Lesson Menu Five-Minute Check (over Lesson 8–6) Then/Now New Vocabulary Key Concept: Slope-Intercept Form Example 1:Find the Slope and y-intercept Example 2:Find Slope and y-intercept Example 3:Graph an Equation Example 4:Analyze the Slope and y-intercept

Over Lesson 8–6 5-Minute Check 1 Find the slope of the line on the graph. A.1 B. C. D.

Over Lesson 8–6 5-Minute Check 2 Find the slope of the line that passes through E(1, 4) and F(5, –2). A. B. C. D.

Over Lesson 8–6 5-Minute Check 3 Find the slope of the line that passes through G(0, –7) and H(2, –7). A.0 B. C.1 D.–1

Over Lesson 8–6 5-Minute Check 4 Find the slope of the line that passes through J(0, 0) and K(4, –4). A.0 B. C.1 D.–1

Over Lesson 8–6 5-Minute Check 5 Find the slope of a line that decreases 4 units vertically for every 10-unit horizontal increase. A. B. C. D.

Over Lesson 8–6 5-Minute Check 6 A hill rises at a vertical distance of 4 feet over a horizontal distance of 24 feet. What is the slope of the hill? A.6 B.3 C. D.

Then/Now You have already graphed linear equations using ordered pairs. (Lesson 8–3) Determine slopes and y-intercepts of lines. Graph linear equations using the slope and y-intercept.

Vocabulary slope-intercept form

Concept

Example 1 Find the Slope and y-intercept Write the original equation. Answer: State the slope and the y-intercept of the graph of

Example 1 A.m = 2; b = –7 B.m = 2; b = 7 C.m = 7; b = 2 D.m = –7; b = 2 State the slope and the y-intercept of the graph of y = 2x – 7.

Example 2 Find Slope and y-intercept State the slope and the y-intercept of the graph of –4x + y = –10. –4x + y=–10Write the original equation. –4x + y + 4x=–10 + 4xAdd 4x to each side. y=–10 + 4xSimplify.

Example 2 Find Slope and y-intercept Write the equation in slope-intercept form. Answer: The slope of the graph is 4 and the y-intercept is –10. y = 4x – 10 m = 4, b = –10

Example 2 A.m = –5; b = 1 B.m = 5; b = 1 C.m = 1; b = 5 D.m = 1; b = –5 State the slope and the y-intercept of the graph of –5x + y = 1.

Example 3 Graph an Equation Graph y = –3x + 9 using the slope and y-intercept. Step 1Find the slope and y-intercept. slope = –3 y-intercept = 9 Step 2Graph the y-intercept point at (0, 9).

Example 3 Graph an Equation Step 4Draw a line through the two points and extend the line. Another point on the line is at (1, 6). Step 3 Use it to locate a second point on the line. Answer:

Example 3 A.Graph a point at (6, 0). Move down two units and right one unit. Draw a line through the two points. B.Graph a point at (6, 0). Move left two units and up one unit. Draw a line through the two points. C.Graph a point at (0, 6). Move up two units and right one unit. Draw a line through the two points. D.Graph a point at (0, 6). Move left two units and up one unit. Draw a line through the two points. How would you graph y = 2x + 6?

Example 4 A Analyze the Slope and y-intercept A. BAKING A class spends $75 on ingredients and then sells cookies for $5 a dozen. The amount earned y can be represented by the equation y = 5x – 75, where x equals the number of dozens sold. Graph the equation. Step 1First, find the slope and the y-intercept. slope = 5 y-intercept = –75

Example 4 A Analyze the Slope and y-intercept Step 2 Plot the point at (0, –75). Since, go up 50 and right 10 and plot another point. Answer: Step 3 Connect these points and extend the line.

Example 4 B Analyze the Slope and y-intercept B. Describe what the y-intercept and the slope represent in the graph. Answer: The y-intercept –75 represents the cost of the ingredients. Slope 5 represents the dollars earned per dozen cookies.

Example 4 CYP A A. T-SHIRTS A T-shirt company spends $150 on materials to make T-shirts and then sells the shirts for $12 each. The amount earned y can be represented by the equation y = 12x – 150, where x represents the number of shirts sold. Graph the equation. A.B. C.D.

Example 4 CYP B A.y-intercept 150 represents number of shirts sold; slope 12 represents cost of materials. B.y-intercept –150 represents cost of materials; slope 12 represents dollars earned per shirt. C.y-intercept 150 represents dollars earned; slope 12 represents cost per shirt. D.y-intercept –150 represents cost of materials; slope 12 represents number of shirts sold. B. Describe what the y-intercept and the slope represent in the graph.

End of the Lesson