Slope and Y-Intercept
Problems
Problems
Linear Forms
3 Digit
Numbers
3 Digit
Numbers
Negatives/Fractions
Inc/Dec
Inc/Dec
Real World
CHALLENGE!!
100
What is the correct slope and y-intercept?
y=3x+5
3 (slope) & 5 (y-intercept)
100
Which form is in STANDARD form?
a. y=3
b. y-5=2x-6
c. 2x-y=2
C
100
y=-2x+3
Is this increasing or decreasing?
decreasing
100
A cab company charges a $3 boarding rate in addition to its meter which is $2 for every mile. Construct the correct linear equation to represent this data.
Y=2x+3
100
3/4y=2x+16
change to slope-intercept form
y=(3/2)x+12
200
What is the correct slope?
y=1/2x+22
1/2
200
How can you convert y=4x+7 into point-slope form?
Find a point on the graph. (0,7), (1,11), etc.
plug the point and slope into the formula
y-11=4(x-1)
200
Either count rise/run = -3/4 or
y2-y1/x2-x1
4-7/4-0
200
A tuxedo rental service charges a $150 flat fee for a suit plus $50 per additional day. Which equation correctly models the total cost of renting the tux for x number of days?
a. y=150x+50
b. y=50x
c. y=50x-150
d. y=50x+150
D! The flat fee would not change, therefore cannot be the coefficient/slope for x. Also, the $150 would not be negative because it is added onto the total cost, NOT subtracted/taken off!
200
Put the following equation in point-slope form:
-(2x+5)/4 = (-4y+16)/8
y-8.5=1(x-2)
300
What is the correct y-intercept?
y=4x+6+17
6+17= 23(y-intercept)
300
How can you rearrange y=5x-4 into standard form
subtract 5x from both sides to get y-5x= -4
300
Which of these graphs has the smallest slope? How can you tell without actually knowing?
The first one because the steeper the graph the smaller the slope.
300
Lin is tracking the progress of her plant' s growth. Today the plant is 5cm high. The plant grows 1.5 cm per day. What is the correct linear equation?
y= 1.5x+5
300
Change to slope intercept form:
(-4-2x)/4 = (9-2y)/3
y=(3/4)x+6
First cross multiply, combine like terms, isolate the variable.
400
What is the correct slope and y-intercept?
y-4=2(x-1)
2
distribute the 2 to get 2x-2, combine like terms by adding 4 to both sides. -2+4=2
400
Change into slope-intercept form
y+5y+8=4x-40
6y+8=4x-40
6y=4x-48
y=(2/3)x -8
400
Graph the following.
y=-3x-1
Is it increasing or decreasing? What is the shift of the graph?
It is decreasing by a rate of down 3 and to the right 1. the graph shifts from the origin down one.
400
Amery has x books that weigh 2 pounds each and y books that weigh 3 pounds each. The total weight of his books is 60 pounds.
a. write the correct linear equation
b. If Amery has 10 3-pounds books, how many 2 pound books does he have?
a. y=-2/3 x +20 (original eqn 2x+3y=60 : use in part b)
b. 15 2-pound books
400
Graph the equation:
(2/5)x-15= (5/8)x-16
First solve (if needed) then graph.
x=50/9 or 5 5/9 vertical line a little past 5.5
500
What is the correct slope and y-intercept?
y-10=2/3(x-6)
Slope: 2/3 Y-Intercept: 14
500
Construct correct equations for all three forms of linear equations
y=5x+4
y-4=3(x-3)
2x-y=2
500
y=4
Is it increasing or decreasing? What is the shift?
It is neither increasing nor decreasing. The graph shifts up 4
500
Create your own word problem for the equation:
y=300x+40,000
ex; A machine salesperson earns a base salary of $40,000 plus
a commission of $300 for every machine he sells.
500
A salesperson receives a base salary of $35,000 and a commission of 10% of the total sales for the year.
a. write a linear equation that shows the salesperson's total income based on total sales of k dollars
b. if the salesperson sells $25,000 worth of merchandise for the year, what is his total income including his base salary?
A; y=.10x (or 1/10 x) + 35,000
B; y=$37,500