Types of Equations
Linear/ Direct Variation Equation
y=mx or y=kx
What is unit rate?
A rate for one of something.
m =
slope
It cost Ms. Fegley $42.11 for 13.1 gallons of gas at Sheetz. What is the unit rate? Round to the nearest cent if necessary.
$3.21 per gallon
The cost, y, of movie tickets and the number of tickets, x, is a proportional relationship. It costs $8.00 per ticket. Write a direct variation equation to represent this relationship.
y=8x
Y-Intercept Form
y=mx+b
What does proportional relationship mean?
A relationship between two quantities in which the ratio of the quantity to the other quantity is constant.
k =
Constant of proportionality/ Slope/ Unit Rate
What is the slope and y-intercept of the equation below? y=3x
Slope: 3
y-intercept: 0, (0,0)
The cost of bulk peanuts varies directly with the weight of the peanuts. At a local grocery store, 2 pounds of peanuts cost $5.80. Write a direct variation equation to represent this relationship.
y=2.9x
Horizontal Line
y = b
Direct variation means when one quantity changes, the other quantity also changes in direct proportion.
y =
y-value in the ordered pair (x,y)
What is the slope and y-intercept of the equation below? y=-2/3x-5
slope: -2/3
y-intercept: -5 , (0,-5)
The table shows the costs for art show participants, including the $30 registration fee. Write an equation in slope-intercept form that represents the data in the table
Number of Pieces of Art: 0 , 2, 4, 6, 8
Cost ($): 30, 90, 150, 210, 270
y=30x+30
Vertical Line
x = c , where c is any real number
What type of slope does the following have?
1. A line going down from the second quadrant to the fourth quadrant.
2. A line going up from the third quadrant to the first quadrant.
1. Negative
2. Positive
x =
x-value in the ordered pair (x,y)
What is the slope and y-intercept of the equation below? y=1/2x-2
Slope: 1/2
y-intercept: -2 (0,-2)
The Augello family is driving from Columbus to St. Louis at a constant rate of 65 miles per hour. The distance between the two cities is 420 miles. Write an equation in slope-intercept form to represent the distance y in miles remaining after driving x hours.
y=-65x+420
What type of equation is this? How do you know?
y=4x+6
y-intercept form
What is the slope of a horizontal line and vertical line?
Horizontal: 0
Vertical: Undefined
b =
y-intercept
What is the slope and y-intercept of the equation below? -3x+y=6
slope: 3
y-intercept: 6 ; (0,6)
Write an equation in slope-intercept form with the given two points.
(0,-3) & (2,1)
y=2x-3