More Direct Variation is represented by a linear function that has a of 0. Direct variation y-intercept Direct variation is represented by a linear graph that goes through the origin. In words, we say varies directly with or is proportional to “y x” “y x”. The ratio of is the which is the same as the slope. y/x constant of variation, For example: if is 3 times as big as then Notice that slope is = 3. y x, y=3x. y/x Examples of direct variation include: Non-Examples of direct variation include: = 3x 1. = 3x + 2 y y = -5x 2. = -6x 3 y y – = ½ 3. = ¼ + 3 y x y x = 4. = 3 y x y x – 5x + 2y = 0 Circle the examples that represent direct variation. a. = b. = 3x 4 y x y – c. = + 1 d. = 2x y x y e. f. Your distance from a lightning strike varies directly with the time it takes you to hear thunder. If you hear thunder 10 seconds after you see lightning, you are about 2 miles from the lightning. What is the independent variable? What is the dependent variable? What is the constant of variation? Write an equation for distance as a function of time. How many miles away is a lightning bolt if you hear the thunder 5 seconds after you see the lightning?
More Direct Variation Direct variation is represented by a linear function that has a y-intercept of 0. Direct variation is represented by a linear graph that goes through the origin. In words, we say “y varies directly with x” or “y is proportional to x”. The ratio of y/x is the constant of variation, which is the same as the slope. For example: if y is 3 times as big as x, then y=3x. Notice that slope is y/x = 3. Examples of direct variation include: Non-Examples of direct variation include: y = 3x 1. y = 3x + 2 y = -5x 2. y = -6x – 3 y = ½ x 3. y = ¼ x + 3 y = x 4. y = x – 3 5x + 2y = 0 Circle the examples that represent direct variation. a. y = x b. y = 3x – 4 c. y = x + 1 d. y = 2x e. f. Your distance from a lightning strike varies directly with the time it takes you to hear thunder. If you hear thunder 10 seconds after you see lightning, you are about 2 miles from the lightning. What is the independent variable? What is the dependent variable? What is the constant of variation? Write an equation for distance as a function of time. How many miles away is a lightning bolt if you hear the thunder 5 seconds after you see the lightning?
alg_u4_i5_a452_more_direct_variation.docx