Solving Linear Equations
Solve the equation: w - 3/5 = -2/5.
w = 1/5
Solve and graph (on separate paper): x - 7 < 2
x < 9
Check graph
See Google Doc
Continuous
Solve the system:
y = 1/2x - 2
y = 4x + 5
(-2,-3)
Write an equation in point-slope form of the line that passes through the point (7,4) and has a slope of 4/9.
y - 4 = 4/9(x - 7)
Solve: -2(x-9) + 2 = 2
x = 9
Solve and graph (on separate paper): x/8 > 9
x > 72
Check graph
Determine whether the equation represents a linear or nonlinear function.
y = -7(x + 4)
Linear
Solve the system:
y = 4x - 7
7x + 4y = -5
(1,-3)
Write an equation in slope-intercept form that passes through (-8,-1) and (-7,3).
y = 4x + 31
Solve |2x + 6| + 1 = 3
x = -2, and x = -4
A pair of wireless headphones costs $160. Your friend has $70 and plans to save $12 each month. Describe the numbers of months your friend needs to save to buy the headphones.
amt. already saved + amt. to save * no. of months > cost of headphones
at least 8 months
Determine whether the equation represents a linear or nonlinear function.
y = x^2 + 5
Nonlinear
Solve the system:
4x - 3y = 1
12x - 15y = -3
(1,1)
Write an equation of the line that passes through (2,-1) that is parallel to the line y = -7x - 8.
y = -7x + 13
You are 5 feet 6 inches tall and cast a shadow 3 feet long. At the same time, a nearby building casts a shadow 30 feet long. Find the height of the building.
h = 55 feet
Solve and graph (on separate paper): 9x - 30 < 5x - 2
x < 7
Check graph
Evaluate f(x) = x + 1 when x = 2
3
Determine the number of solutions of the system.
3x - 4y = 9
12x + 8y = 36
One solution
Write the equation of the line that passes through (8,-7) and is perpendicular to the line y = 8x - 7.
y = -1/8x - 6
Two shops each charge a rental fee plus an hourly fee to rent a canoe. How many hours must a canoe be rented for the total costs at both shops to be the same?
Shop A: Shop B:
Rental Fee: $2 $8
Hourly Fee: $5 $4
6 hours
Solve and graph (on separate paper): 6x - 20 < 4x - 8
x < 6
Evaluate f(x) = 3x + 9 when x = -3
0
You buy 6 health bars and 2 health drinks for $22. Your friend buys 5 health bars and 3 health drinks for $21. What is the cost of each health bar? What is the cost of each health drink?
Bar: $3
Drink: $2
Write an equation for the nth term of the arithmetic sequence -4, 1, 6, 11, ...Then find a(25).
a(n) = 5n - 9; a(25) = 116