Determine the slope of the line that passes

Math 8 H 4 -2 Slope and Direct Variation Algebra 1 Glencoe Mc. Graw-Hill

A direct variation equation is a special type of linear equation. Every direct variation

When two quantities have a constant ratio, they are said to have a direct

Slope is the ratio of the change in y to the change in x.

Solve the direct variation equation for y. A direct variation equation represents a constant

(1, 3) (0, 0) This is a graph of the direct variation equation y

This is a graph of the (4, 1) (0, 0) direct variation equation y=

Remember: every direct variation equation will graph as a line that passes through the

Graph y = 5 x y • • 1. Write the slope as a

Graph y = x y • x • 1. The slope is already a

Y varies directly as x. Write a direct variation equation that relates x and

The cost of bananas varies directly with their weight. If 3 pounds of bananas

d = rt is a direct variation equation! Distance (d) varies directly as time

Use the direct variation equation to find how long will it take for the

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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 .

Math 8 H 4 -2 Slope and Direct Variation Algebra 1 Glencoe Mc. Graw-Hill Jo. Ann Evans

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

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”.

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 k is the slope of the line.

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

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

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

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

Graph y = 5 x y • • 1. Write the slope as a ratio. x 2. Plot a point at (0, 0). 3. Walk the slope. A slope of tells you to go UP 5, OVER 1. 4. Plot the point. Connect the two points with a line.

Graph y = x y • x • 1. The slope is already a ratio. Assign the negative to the numerator. 2. Plot a point at (0, 0). 3. Walk the slope. A slope of tells you to go DOWN 3, OVER 4. 4. Plot the point. Connect the two points with a line.

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

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. Use this information to write the direct variation equation. Using the equation, answer the question. x equals 12 when y = 108.

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. Use this information to write the direct variation equation. Using the equation, answer the question. x equals 29 when y = -87.

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. Use this information to write the direct variation equation. Using the equation, answer the question. y equals -4. 5 when x = -. 3.

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. Use this information to write the direct variation equation. Using the equation, answer the question. x equals 24 when y = -16.

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.

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) 62 = r The balloon’s ascent rate is 62 feet per minute. d = 62 t is the direct variation equation.

Use the direct variation equation to find how long will it take for the balloon to rise 1209 feet. d = 62 t (1209) = 62 t 19. 5 = t The balloon should ascend 1209 feet in 19. 5 minutes.