Given the table for x, lawns mowed, and y, money earned:
x - # of lawns mowed 7 6 2 9 3
y - $ earned 294 252 84 378 126
Match the equation type with the correct equation for this table.
Standard form
Slope-intercept form
Point-Slope form
y = -42x + 2
y = 42x
y = x + 42
6x - 252y = 42
2x + 84y = 42
42x - y = 0
(y - 84) = 42(x - 2)
(y + 126) = 42(x + 3)
(y - 7) = 42(x - 294)
Standard form: 6x - 252y = 42
Slope-intercept form: y = -42x + 2
Point-Slope form: (y - 84) = 42(x - 2)
Change the equation from standard form to slope-intercept form by solving for y. 11x - 8y = -48
Bob: Subtract 11x from both sides: -8y = -59x Divide by -8 on both sides: y = 7.375
Bill: Subtract 11x from both sides: -8y = -11x - 48 Divide by -8 on both sides: y = 11/8 x + 6
Bud: Subtract 11x from both sides: -8y = -11x - 48 Divide by -8 on both sides: y = -11x + 6
Who is correct?
Bob
Bill
Bud
None of them are correct
All of them are correct
Bill is correct. The correct answer is y = 11/8 x + 6.
Suppose that the water level of a river is 34 feet after 3 days of rain and 62 feet after 10 days of rain. The river was 22 feet before the rain began.
What is the rate of change for this scenario?
What is the y-intercept for this scenario?
Write an equation in Point-slope form.
Change that equation to Standard form.
4
1/4
12
(0, 0)
(0, 22)
(3, 34)
(10, 62)
(y - 34) = 4(x + 3)
(y - 10) = 1/4(x - 62)
(y - 62) = 4(x - 10)
4x - y = -22
3x + 34y = 22
10x - 62y = 22
The rate of change for this scenario is 4.
The y-intercept for this scenario is (0, 22).
Equation in Point-slope form: (y - 34) = 4(x + 3).
Changing that equation to Standard form: 4x - y = -22.
A cab company charges $8 per mile for a lift to the airport, which is proportional since 0 miles cost $0.
What change would the company make to their charges to make this a nonproportional situation?
Charge $12 per mile instead of $8
Charge $4 per mile instead of $8
No changes are needed
Charge a flat rate of $10 and then $8 per mile
Charge no flat rate and no $ per mile
Charge a flat rate of $10 and then $8 per mile. Making a flat rate in addition to the per-mile charge would make it a nonproportional situation.
Solve 2x + b = c for x.
2x + b - b= c - b subtract b from both sides
2x = c - b combine like terms/simplify
2x - 2= c - b - 2 subtract 2 from both sides to get x isolated
x = c - b - 2 simplify/final answer
Which statement is true?
The process has an error. The correct answer is: x = (c - b) / 2
The process has an error. The correct answer is: x = c/2 - b
The process is correct.
The process has an error. The correct answer is: x = c + b - 2
The process has an error. The correct answer is: x = (c - b) / 2.
Put the steps in order to solve this equation for y: 4 (y + 10) = 3 (x - 2)
4y = 3x − 46
4y + 40 = 3x − 6
y = (3x − 46) ÷ 4
y = 34x − 11.5