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

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Over Lesson 8–6 A.A B.B C.C D.D 5-Minute Check 1 Find the slope of the line that passes through E(1, 4) and F(5, –2). Find the slope of the line that passes through G(0, –7) and H(2, –7). Find the slope of the line that passes through J(0, 0) and K(4, –4).

Splash Screen

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 A linear equation in the form y = mx + b, where m is the slope and b is the y- intercept.

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

A.A B.B C.C D.D 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

A.A B.B C.C D.D 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:

A.A B.B C.C D.D Example 3 Graph y = 2x – 3.

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.

A.A B.B C.C D.D 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.

A.A B.B C.C D.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