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The lingo
Story time
To vary directly or not to vary directly
Get to the point
Intercepted
100
Define y-intercept.
The y-coordinate of a point where the graph crosses the y-axis; (0, y)
100
A salesperson earns $18 per hour plus a $75 bonus for meeting her sales quota. Write an equation that represents her total earnings, including her bonus. What does the independent variable represent? What does the dependent variable represent?
y=18x + 75; y = total earnings (dependent); x = # of hours (independent)
100
Determine whether the equation represents a direct variation. If it does, find the constant of variation. 3x+4y=-5
no
100
Write an equation for the line in point-slope form that passes through the given point and has the given slope m: (2, -2); m =-1/2
y+2=(-1/2)(x-2)
100
Write an equation in point-slope form for the line that passes through the given point and has the given slope m: (-3, -6); m = -1
y=-x-9
200
Define slope.
The slope of the line is the ratio of the vertical change (the rise) to the horizontal change (the run).
200
Hudson is already 40 miles away from home on his drive back to college. He is driving 65 mi/h. Write an equation that models the total distance d traveled after h hours. What does the independent variable represent? What does the dependent variable represent?
d=65h+40; d=distance traveled (dependent) h=hours (independent)
200
Determine whether the equation represents a direct variation. If it does, find the constant of variation. 5x+12.5y=0
yes; -2/5 or -0.4
200
Write an equation in point-slope form for the line that passes through the given point and has the given slope m: (4, 0); m = 4
y=4(x-4)
200
Write an equation in slope-intercept form for the line that passes through the given points: (2, 5) and (-8, 5)
y=5
300
What is the slope-intercept form of a linear equation?
The slope-intercept form of a linear equation is y=mx+b, where m is the slope and b is the y-intercept.
300
Jade has run the first 4 miles of a race in 30 minutes. She reached the 6 mile point after 45 minutes. What is the slope?
2/15 mi/min or 8 mi/h
300
Suppose y varies directly with x. Write a direct variation equation that relates x and y when y = 15 and x = 6. then find the value of y when x = 7.
y=(1/3)x; y=7/3
300
Write an equation in point-slope form for the line that passes through the given point and has the given slope m: (-1,-5); m = 5
y+5=5(x+1)
300
Write an equation in slope-intercept form for the line that passes through the given points: (7, 3) and (5, 1)
y=x-4
400
What is the point-slope form of a linear equation?
The point-slope form of a linear equation is y-y1=m(x-x1), where m is the slope and (x1, y1) is a point on the line.
400
The amount, a, you fill a tub varies directly with the amount of time, t, you fill it. Suppose you fill 25 gallons in 5 minutes. What is an equation that relates a and t.
a=5t
400
Suppose y varies directly with x. Write a direct variation equation that relates x and y when y = 14 and x = -4. Then find the value of y when x = -6.
y=-3.5x or y=(7/2)x; y=21
400
Write an equation in point-slope form for the line that passes through the given points: (4, -2) and (8, -6)
y+2=-1(x-4) or y+6=-1(x-8)
400
Write an equation in slope-intercept form for the line that passes through the given points: (4, -2) and (8, -6)
y=-x+2
500
What is a direct variation?
A direct variation is a relationship that can be represented by a function in the form y=kx, where k does not equal 0. The graph of a direct variation equation is a line that passes through the origin and has slope k.
500
A sign says that 3 tickets cost $22.50 and that 7 tickets cost $52.50. Write an equation in point-slope form that represents the cost of the tickets.
y-22.5=7.5(x-3)
500
Stephanie gets paid $16.75 per hour at her job. Write a direct variation equation where h represents the number of hours she works and d represents the amount of money she earns. Graph the equation.
d=16.75h
500
Graph the following equation: y+3=(1/2)(x+2)
See separate sheet.
500
Graph the following equation: y=4x-3
See separate sheet.