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4-2 Warm Up

4-2 Warm Up. Determine the slope of the line that passes through each pair of points: (3, 5) and (7, 12) (-2, 4) and (5, 4) (-3, 6) and (2, -6) (7, -2) and (7, 13).

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4-2 Warm Up

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  1. 4-2 Warm Up Determine the slope of the line that passes through each pair of points: (3, 5) and (7, 12) (-2, 4) and (5, 4) (-3, 6) and (2, -6) (7, -2) and (7, 13) Determine the value of n so that the slope of the line through (n, 4) and (1, n) is .

  2. Math 8H 4-2 Slope and Direct Variation Algebra 1 Glencoe McGraw-Hill JoAnn Evans

  3. A direct variation equation is a special type of linear equation. Every direct variation equation will graph as a line that passes through theorigin. (0, 0) y x

  4. When two quantities have a constant ratio, they are said to have a direct variation. The two quantities will be represented as y and x. Written in ratio form the ratio of y to x is . What ratio did we study in the previous lesson? SLOPE! In direct variation equations, the slope has a different name. It is known as the “constant of variation”.

  5. Slope is the ratio of the change in y to the change in x. A direct variation equation is: In a direct variation equation k is called the constant of variation. On the graph of a direct variation equation kis the slope of the line.

  6. Solve the direct variation equation for y. A direct variation equation represents a constant rate of change. “k” is the constant of variation

  7. This is a graph of the direct variation equation y = 3x. The constant of variation is 3. (1, 3) (0, 0) What is the slope of the line? The slope of the line is the same as the constant of variation.

  8. This is a graph of the direct variation equation y = x. What is the constant of variation? (4, 1) (0, 0) What is the slope of the line? The slope of the line is the same as the constant of variation.

  9. Remember: every direct variation equation will graph as a line that passes through theorigin. y x

  10. Graph y = 5x y • • Write the slope as a ratio. • x 2. Plot a point at (0, 0). • Walk the slope. A slope • of tells you to go • UP 5, OVER 1. • Plot the point. • Connect the two points with a line.

  11. Graph y = x y • The slope is already a ratio. Assign the negative to the numerator. • x 2. Plot a point at (0, 0). • • Walk the slope. A slope • of tells you to go • DOWN 3, OVER 4. • Plot the point. • Connect the two points with a line.

  12. Graph y = x Graph y = -x y y • • • x x • What is the slope? It’s -1. Written as a ratio, that’s .

  13. Y varies directly as x. Write a direct variation equation that relates x and y. If y = -27 when x = -3, find x when y = 108. Using the equation, answer the question. Use this information to write the direct variation equation. x equals 12 when y = 108.

  14. Y varies directly as x. Write a direct variation equation that relates x and y. If y = -15 when x = 5, find x when y = -87. Using the equation, answer the question. Use this information to write the direct variation equation. x equals 29 when y = -87.

  15. Y varies directly as x. Write a direct variation equation that relates x and y. If y = 7.5 when x = 0.5, find y when x = -0.3. Using the equation, answer the question. Use this information to write the direct variation equation. y equals -4.5 when x = -.3.

  16. Y varies directly as x. Write a direct variation equation that relates x and y. If y = 12 when x = 18, find x when y = -16. Using the equation, answer the question. Use this information to write the direct variation equation. x equals 24 when y = -16.

  17. The cost of bananas varies directly with their weight. If 3 pounds of bananas cost $2.04, find the cost of 4 pounds. Write a direct variation equation that relates the cost, c, to the weight, w. Use the equation to answer the question. If c = $2.04 when w = 3, find c when w = 4. The cost is $2.72 for 4 lb. of bananas.

  18. d = rt is a direct variation equation! Distance (d) varies directly as time (t). The rate (r) is the constant of variation. A hot air balloon’s distance of ascent varies directly as the time. The balloon ascended 372 feet in six minutes. Write a direct variation equation that relates the distance, d, to the time, t. d = rt (372) = r(6) The balloon’s ascent rate is 62 feet per minute. 62 = r d = 62t is the direct variation equation.

  19. Use the direct variation equation to find how long will it take for the balloon to rise 1209 feet. d = 62t (1209) = 62t 19.5 = t The balloon should ascend 1209 feet in 19.5 minutes.

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