Using Slopes and Intercepts

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1 CODE Name Date Teacher Practice A Using Slopes and Intercepts 1. Name the ordered pair if the x-intercept is Name the ordered pair if the y-intercept is In the ordered pair (9, 0), what is the x-intercept? 4. In the ordered pair (0, 0), what is the relationship of the x-intercept and y-intercept? Find the x-intercept and y-intercept of each line. Use the intercepts to graph the equation. 5. x + y = x y = 6 _ Write each equation in slope-intercept form, and then find the slope and y-intercept. 7. 2x + y = 5 8. x y = x 2y = 4 Write the equation of the line that passes through each pair of points in slope-intercept form. 10. (1, 2), ( 1, 0) 11. (1, 3), ( 1, 1) 12. (1, 1), ( 3, 3)

2 CODE Name Date Teacher Practice B Using Slopes and Intercepts Find the x-intercept and y-intercept of each line. Use the intercepts to graph the equation. 1. x y = x + 3y = 12 Write each equation in slope-intercept form, and then find the slope and y-intercept. 3. 3x + y = x y = x 5y = 10 Write the equation of the line that passes through each pair of points in slope-intercept form. 6. (3, 4), (4, 6) 7. ( 1, 1), (2, 10) 8. (6, 5), ( 9, 20) 9. A pizzeria charges $8 for a large cheese pizza, plus $2 for each topping. The total cost for a large pizza is given by the equation C = 2t + 8, where t is the number of toppings. Graph the equation for t between 0 and 5 toppings, and explain the meaning of the slope and y-intercept. CODE Practice C Using Slopes and Intercepts Original content Copyright by EduPro, Inc.

3 Name Date Teacher Find the x-intercept and y-intercept of each line. Use the intercepts to graph the equation. 1. 3x 2y = x + 4y = 20 _ Write each equation in slope-intercept form, and then find the slope and y-intercept. 3. y 3x = y 2x = y 2x = 1 2 Write the equation of the line that passes through each pair of points in slope-intercept form. 6. (3, 4), ( 1, 4) 7. (6, 10), (12, 14) 8. (9, 3), (9, 5) 9. A home improvement warehouse charges a $60 delivery fee. A customer wants to purchase a number of pieces of lumber that cost $5 a piece. Write an equation in slope-intercept form, where C is the total cost of the delivered lumber and x represents the number of pieces of lumber purchased. Graph the equation for x between 1 and 5 pieces, and explain the meaning of the slope and y-intercept. CODE Review for Mastery Using Slopes and Intercepts

4 Name Date Teacher x-intercept: the x-coordinate of the point at which a line crosses the x-axis y-intercept: the y-coordinate of the point at which a line crosses the y-axis You can find the intercepts of a line from its equation. Then you can use the intercepts to graph the line. Find the intercepts of the line 3x + 4y = 24. For the x-intercept, For the y-intercept, let y = 0. let x = 0. 3x + 4y = 24 3x + 4y = 24 3x + 4(0) = 24 3(0) + 4y = 24 3x + 0 = y = 24 3x = 24 4y = 24 3x 3 = 24 4y 3 4 = 24 4 x = 8 y = 6 The x-intercept is 8. The y-intercept is 6. Find the intercepts of each line. Draw both graphs on the same grid. 1. 2x + 3y = 12 for x-intercept for y-intercept 2x + 3( ) = 12 2( ) + 3y = 12 x = y = 2. 6y 3x = 6 for x-intercept for y-intercept 6( ) 3x = 6 6y 3( ) = 6 x = y =

5 LESSON Name Date Teacher Review for Mastery Using Slopes and Intercepts (continued) slope-intercept form To rewrite an equation in slope-intercept form, isolate y. y = mx + b 2x + 3y = 12 2x 2x Subtract 2x. slope y-intercept 3y = 2x 12 3y 3 = 2 3 x 12 Divide by 3. 3 In this form, the coefficient of x is the slope and the constant term is the y-intercept. y = 2 3 x 4 So, m = 2 3 and b = 4. Write each equation in slope-intercept form and then find the slope and y-intercept. 3. 3y = 4x x 2y = 6 Subtract 3x. _ Given two points of a line, you can write its equation. (2, 5) and ( 1, 4) slope = y y 2 1 = 4 5 x 2 x = 9 3 = 3 To find b, substitute the slope and the values from one of the points into the slope-intercept equation. y = mx + b 5 = 3(2) + b 5 = 6 + b 1 = b So, the equation for the line that passes through (2, 5) and ( 1, 4) is y = 3x 1. _ Write the equation of the line that passes through each pair of points in slope-intercept form. 5. (2, 11) and (0, 3) 6. ( 1, 3) and (4, 2) 7. (10, 1) and (6, 1)

6 CODE Name Date Teacher Challenge Another View The intercepts of a line are the points where the line crosses the coordinate axes. When an equation was in standard form, you found the intercepts by setting one variable and then the other equal to zero. 1. Find the intercepts of the line whose equation is 3x + 5y = 15. For the x-intercept, For the y-intercept, let y = 0. let x = 0. The x-intercept is. The y-intercept is. When an equation is in standard form, you can also find the intercepts by dividing both sides by the constant (on the right side). 2. Divide both sides of the equation 3x + 5y = 15 by 15, and simplify. Compare the results to those obtained in Question Using b to represent the y-intercept and a to represent the x-intercept, write an equation that generalizes the observation you made in Question a. Using the form of the equation you wrote in Question 3, find the intercepts of the linear equation 2x + 3y = 24. The x-intercept is and the y-intercept is. b. Check your result by using the first method to find the intercepts.

7 CODE Name Date Teacher Problem Solving Using Slopes and Intercepts Write the correct answer. 1. Jaime purchased a $20 bus pass. Each time she rides the bus, $1.25 is deducted from the pass. The linear equation y = 1.25x + 20 represents the amount of money on the bus pass after x rides. Identify the slope and the x- and y-intercepts. Graph the equation at the right. 2. The rent charged for space in an office building is related to the size of the space rented. The rent for 600 square feet of floor space is $750, while the rent for 900 square feet is $1150. Write an equation for the rent y based on the square footage of the floor space x. Choose the letter of the correct answer. 3. A limousine charges $35 plus $2 per mile. Which equation shows the total cost of a ride in the limousine? A y = 35x + 2 C y = 2x 35 B y = 2x + 35 D 2x + 35y = 2 5. A friend gave Ms. Morris a $50 gift card for a local car wash. If each car wash costs $6, which equation shows the number of dollars left on the card? A 50x + 6y = 1 C y = 6x + 50 B y = 6x + 50 D y = 6x A newspaper delivery person earns $75 each day plus $0.10 per paper delivered. Which equation shows the daily earnings of a delivery person? F y = 0.1x + 75 H x + 0.1y = 75 G y = 75x J 0.1x + y = Antonio s weekly allowance is given by the equation A = 0.5c + 10, where c is the number of chores he does. If he received $16 in allowance one week, how many chores did he do? F 10 H 14 G 12 J 15

8 CODE Name Date Teacher Reading Strategies Use a Visual Model Refer to the coordinate plane at the right. Find the point where the line crosses the x-axis. This point is called the x-intercept. 1. What is the y-value of the ordered pair for this point? Find the point where the line crosses the y-axis. This point is called the y-intercept. 2. What is the x-value of the ordered pair for this point? 3. Which axis does the line cross at the x-intercept? 4. Name the ordered pair for the point where the line crosses the x-axis. 5. Which axis does the line cross at the y-intercept? 6. Name the ordered pair for the point where the line crosses the y-axis.

diagonally). Find a word that answers the riddle.

9 Name Date Teacher CODE Puzzles, Twisters & Teasers Word Bath! Circle words from the list in the word search (horizontally, vertically or diagonally). Find a word that answers the riddle. intercept slope form graph coordinate axis point line rate change Why did the robber take a bath? Because he wanted to make a getaway.

10 Name Date Teacher ANSWER 1. Practice A 1. ( 2, 0) 2. (0, 8) x-intercept = y-intercept x-intercept is 3; y-intercept is 3 6. x-intercept is 5; y-intercept is 5 x-intercept is 3; y-intercept is 6 7. y = 2x 5; 8. y = x 10; m = 2; b = 5 m = 1; b = y = 1 x 2; 10. y = x m = 1 2 ; b = y = 2x y = x Practice B x-intercept is 6; y-intercept is 4 3. y = 3x; m = 3; b = 0 4. y = 2x + 15; m = 2; b = y = 1 5 x 2; m = 1 5 ; b = 2 6. y = 2x 2 7. y = 3x 4 8. y = 5 3 x 5 9. The y-intercept represents the cost of a pizza with no toppings. The slope represents the rate of change ($2 per topping).

11 Name Date Teacher 9. C = 5x + 60; The slope represents the rate of change ($5 per piece of lumber). The y-intercept represents the delivery fee ($60). Practice C 1. x-intercept is 2; y-intercept is 3 2. Review for Mastery x = 12 2x 2 = y = 12 3y 3 = x-intercept is 6; y-intercept is 4 3. y = 3x; m = 3; b = 0 4. y = 2x + 15; m = 2; b = y = 1 5 x 2; m = 1 5 ; x-intercept is 4; y-intercept is 5 3. m = 3; b = m = 2 3 ; b = 3 5. m = 1 3 ; b = y = 2x 2 7. y = 2 3 x y = 9 b = 2 6. y = 2x 2 7. y = 3x 4 8. y = 5 3 x 5 9. The y-intercept represents the cost of a pizza with no toppings. The slope represents the rate of change ($2 per topping).

Name Date Teacher 4. F 5. C 6. G Reading Strategies 1. 0 2. 0 3. the x-axis 4. (9, 0) 5. y-axis 6.

12 Name Date Teacher 4. F 5. C 6. G Reading Strategies the x-axis 4. (9, 0) 5. y-axis 6. (0, 6) Puzzles, Twisters & Teasers Problem Solving 1. x-intercept = 16, y-intercept = 20, slope = 1.25 clean 2. y = 4 x B 3

E. Slope-Intercept Form and Direct Variation (pp )

E. Slope-Intercept Form and Direct Variation (pp ) and Direct Variation (pp. 32 35) For any two points, there is one and only one line that contains both points. This fact can help you graph a linear equation. Many times, it will be convenient to use the