Linear and Non-Linear Relations
Given the table of values below, determine if the relation is linear or non-linear
x: 1, 2, 3, 4
y: 2, 4, 6, 8
Linear
A $1000 investment earns simple interest at a rate of 5% per year. How much interest is earned after 3 years?
$150
Find the slope of a line with rise = 6 and run = 3.
m = 2
Write the equation of a line with slope m = 3 and y-intercept b = -2.
y = 3x - 2
Determine whether the line is horizontal, vertical, or neither: y = -3
Horizontal
Classify the relation as linear or non-linear.
y = 5x² + 1
Non-linear
A $2000 investment earns simple interest at a rate of 4% per year. Find the total amount after 5 years.
$2400
Determine the slope of the line passing through the points (2, 4) and (6, 12).
m = 2
Determine the equation of the line with slope m = -4 that passes through the point (0, 7).
y = -4x + 7
Determine whether the line is horizontal, vertical, or neither: x = 8
Vertical
Determine if the relation is linear or non-linear by using first differences.
x: -2, -1, 0, 1, 2
y: 4, 1, 0, 1, 4
Non-linear
A $1500 investment is compounded annually at a rate of 6%. Find the value after 2 years.
$1685.40
Find the slope between the points (-3, 5) and (1, -3).
m = -2
Find the equation of the line that passes through the points (1, 2) and (3, 6).
y = 2x
Determine whether the pair of lines are parallel, perpendicular, or neither:
y = 4x + 1
y = 4x - 9
Parallel
A relation is given by the points (0, 3), (1, 6), (2, 9), (3, 15).
Determine whether the relation is linear or non-linear. Justify using first differences.
Non-linear (first differences: +3, +3, +6 → not constant)
A laptop depreciates by 10% each year. Its initial value is $1200.
a) Write an equation to model the value after t years
b) Find the value after 3 years
a) V = 1200(0.9)^t
b) $874.80
A line passes through the point (4, 1) and has a slope of 5. Determine another point on the line.
Example: (5, 6)
Rearrange the equation 6x - 3y = 12 into the form y = mx + b. State the slope and y-intercept.
y = 2x - 4
m = 2
b = -4
Determine whether the pair of lines are parallel, perpendicular, or neither:
y = -2x + 5
y = (1/2)x - 3
Perpendicular
A relation has an initial value of 5 and increases by 3 each time x increases by 1.
a) Write a table of values for x = 0 to 4
b) Determine if the relation is linear or non-linear
c) Write the equation of the relation
a) x: 0,1,2,3,4 y: 5,8,11,14,17
b) Linear
c) y = 3x + 5
A $5000 investment is compounded annually at 8%.
a) Write an equation to model the investment after t years
b) Determine the value after 4 years
c) Is this linear or exponential growth?
a) A = 5000(1.08)^t
b) $6802.44
c) Exponential growth
A line passes through the points (3, 7) and (14, k) and has a slope of 5/11. Determine the value of k.
k = 12
A gym charges a $25 sign-up fee and $15 per month.
a) Write an equation to model the total cost y after x months
b) How much will it cost after 8 months?
c) How many months will it take to cost $160?
a) y = 15x + 25
b) y = 15(8) + 25 = 145
c) x = 9 months
Write the equation of a line that is perpendicular to y = 3x - 4 and passes through the point (2, 1).
y = (-1/3)x + 5/3