Nonproportional Linear Relationships
For the linear function g(x) = 5x - 2 identify the slope and the y-intercept
slope is 5 and y-intercept is -2
What is the slope intercept form of a linear equation?
y = mx + b
In the expression x/4 - 6 what operations happened to x and in what order?
x was divided by 4 then 6 was subtracted from the result
Solve for x
y = 5x - 8
x = (y + 8)/5
The sum of two consecutive integers is 37. Find both integers
18 and 19
For the function f(x) = -5x + 2 evaluate the function at x = -2.5
14.5
Rewrite in y = mx + b form
-2x + y = 1
y = 2x + 1
Determine whether each of the following values for the given variable is a solution to the given equation.
4(x - 3) + 5 = 17 and x = 5
no
Solve for b:
a = m/b
b = m/a
The sum of 3 consecutive odd integers is 81. Find the 3 integers
25, 27, 29
Which of the following represents the average rate of change of the function f(x) = (4/5)x + 2 over the interval 1 < x < 5
4/5
Rewrite in y = mx + b
3y - 2x = 9
y = (2/3)x + 3
Solve for x:
7x - 9 = 3(x + 6) + 1
x = 7
Solve for x
A = 3x + 2bx
x = A/(3+2b)
The sum of three times a number and 1 less than 5 times that same number is 15. Find the number.
2
What is the equation of a line whose slope is 3 and which passes through the point (3, 10)
y = 3x + 1
Write an equation for the line that passes through the points (1, 1) and (3, 5)
y = 2x - 1
3/4 (8x-4) - 5 = 1/2 (4x + 6)
x = 11/4
Solve for y:
P = 4(x + y) - 3y
y = P - 4x
Liam is 4 years older than his sister, Emma. In 6 years, the sum of their ages will be 42 years.
How old are Liam and Emma now?
13 and 17
Define a proportional relationship between x and y
The variables x and y are proportional if y/x = k or y = kx. Or, if one variable is always a constant multiple of the other
Write an equation that goes through the points (-4, 2) and (1, -5)
y = (-7/5)x - (18/5)
Solve for x:
(2x-5)/3 + (x+4)/2 = (5x-1)/6 + 7
x = 39/2
Solve for r:
(1/f)= (1/d)+(1/r)
r = (fd)/(d-f)
The length of a rectangle is 7 feet more than twice its width. If the perimeter of the rectangle is 74 feet, find the dimensions of the rectangle.
width = 10 ft and length = 27 ft