Direct Variation and slope
4/5
Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. If he counted four seconds between the next flash of lightning and thunder, about how far away was the lightning?
5/7
Find the slope between the two points. (3, 7) and (-4, 2)
-1/5
Find the slope of the line that passes through (10, 1) and (5, 2)
-6
Find the zero of the function f(x) = 2x + 12
11
Given two ordered pairs (7, 3), (x, 4) and a slope of ¼, calculate the missing value x.
26
In a direct variation, y=39 when x=3. Find the value of y when x=2.
6
Ohm's Law states that the voltage, V, of an electrical circuit is directly proportional to I, the current. If the current was 1.3 amps when the voltage was 2.6 volts, what would the current be when if the voltage was increased to 12 volts?
27
On a treasure map, the actual distance is directly related to the scaled distance. If 15 miles is represented by 3 centimeters, then how many centimeters on the treasure map are equivalent to 135 miles?
origin
Proportional and direct variation equations pass through the ________.
Proportional
Proportional or non-proportional? y = 2x
Non-proportional
Proportional or non-proportional? y = 3x + 8
average rate of change
Slope is also known as the....
308
The amount of money earned on a job is directly proportional to the number of hours worked. If $70.00 is earned in 5 hours, how much money is earned in 22 hours of work?
225
The gas pressure in a chamber varies directly with the temperature in the chamber. If the pressure in the chamber is 150 atmospheres (atm) when the chamber is at 50 degrees, what is the pressure in the chamber when the temperature of the chamber is 75 degrees?
90
The interest received on a savings account varies directly with the amount deposited. Daniel received $55.35 in interest on $1230 he deposited. How much interest would Daniel have received if he had deposited $2000 into his account?
777
The money made tutoring directly varies with the time spent tutoring. If a tutoring job pays $222 for 10 hours of work, how much would they make for 35 hours of work?
20
The number of words Maria typed varied directly with the amount of time she spent typing. If she typed 275 words in 5 minutes, how long would it take her to type 1,100 words?
394
Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours?
y = 3
What is the equation of a horizontal line that passes through (10, 3)?
y = 10
What is the equation of a horizontal line that passes through (3, 10)?
x = 10
What is the equation of a vertical line that passes through (10, 3)?
x = 3
What is the equation of a vertical line that passes through (3, 10)?
0
What is the slope of a horizontal line?
undefined
What is the slope of the equation x = 4?
-7
What is the solution to y = 7 + x
-8
What is the value of y if (2, y) is a solution to the equation 4x - 2y =24?
(5, 0) and (0, -2)
What is the x and y intercept for the following equation ? 4x - 10y = 20
(3, 0) and (0, -5)
What is the x and y intercept for the following equation ? 5x - 3y = 15
2
What is the y-intercept of x + 2y = 4
Vertical
What kind of line has an undefined slope?
Horizontal
What kind of line has an zero slope?
(0, 0)
What ordered pair does a direct variation equation always go through when graphed?
x-intercept
What term is the same as roots, zeroes, and solutions?
60
y varies directly with x, and y is 15 when x is 9. What is y when x is 36?
y = ½x
y varies directly with x, and y is 16 when x is 32. Which equation represents this situation?
k = 10
y varies directly with x, and y is 40 when x is 4. What is the constant of variation?
16
y varies directly with x, and y is 5 when x is 10. What is x when y is 8?
y = ¼x
y varies directly with x, and y is 7 when x is 28. Which equation represents this situation?
y = 4x
y varies directly with x, and y is 8 when x is 2. Which equation represents this situation?
k = 5
y varies directly with x, and y is 80 when x is 16. What is the constant of variation?
190.65
A person's weekly pay is directly proportional to the number of hours worked. Shawn's pay is $123.00 for 20 hours of work. Find the amount of pay for 31 hours of work.
constant rate of change
Another phrase for slope is
-1
Determine "r" if the slope is undefined: (r, 3), (-1, 5)
-3
Determine "r" if the slope is zero: (-4, -3), (-1, r)
k = 8
Determine the constant of variation: y = 8x
k = 9
Determine the constant of variation: y = 9x
(8, 0)
Determine the roots: 3x + 8y = 24
-2
Determine the roots: 3x + y = -6
-5/3
Determine the slope of the line passing through the points (2, 1) and (5, -4).
(15/2, 0)
Determine the x-intercept: 2x - 3y = 15
(0, -5)
Determine the y-intercept: 2x - 3y = 15