Equations of Linear Functions
Write an equation of a line in slope-intercept form that passes through the given point and has the given slope.
(-4,2); slope -3
y = -3x - 10
Define a variable, write an inequality, and solve the problem.
Nine times a number decreased by four is at least twenty three.
9x - 4 > 23; x > 3
How many solutions? If it has one solution, what is it?
x - y = 4
x + y = -10
one; (7,3)
Simplify: (5a7bc2)(-6a2bc5)
-30a9b2c7
A person walked 1.5 miles in 28 minutes and then jogged 1.2 more miles in 10 minutes. What was the average speed in miles per minute?
0.07 mi/min
Find the inverse:
f(x) = 4x + 10
f-1(x) = .25x - 5/2
Solve:
|2f + 7| > 21
f > 7 or f < 14
Use substitution to solve:
x = -4y - 3
3x - 2y = 5
(1,-1)
Write in scientific notation
0.00021
2.1 x 10-4
A boat travels 36 mph in 1.5 hours and then 14 miles in 0.75 hour. What is the average speed of the boat?
22.2 mph
Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of each equation.
(2,-3) y = 4x - 9
y = 4x - 11
Solve
-2(x - 4) > 5x - 13
{x|x < 3}
Use elimination to solve:
2x + 6y = 18
3x + 2y = 13
(3,2)
Solve 9x-3 = 729
x = 6
A lab technician has 40 gallons of a 15% iodine solution. How many gallons of a 40% iodine solution must he add to make a 20% iodine solution?
10 gallons
Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the graph of the equation.
(-3,6) y = 0.25x + 2
y = -4x - 6
Graph y > -2x + 5 then determine which of the ordered pairs are in the solution set: (-2,0) (-1,5) (2,3) (7,3)
(2,3) (7,3)
Shelly has $175. Each pair of jeans costs $25, each sweater costs $20, and she buys 8 items. How many jeans and sweaters did she buy?
3 jeans, 5 sweaters
Find the next three terms in the sequence:
2, -6, 18
-54, 162, -486
Margo has 40 milliliters of 25% solution. How many milliliters of 60% solution should she add to obtain the required 30% solution?
about 6.67 mL
Write an equation in slope-intercept form that passes through the given points.
(2,5) (-2,8)
y = -3/4x + 13/2
Mrs.Jones is buying new books and puzzles for her class. Each book costs $6, and each puzzle costs $4. Write and graph an inequality to determine how many books and puzzles she can buy for $96.
Line passing through (6,16) and (12,6).
At a sale, Joaquin bought 24 reams of paper and 4 inkjet cartridges for $320. Britney bought 2 reams of paper and 1 inkjet cartridge for $50. The reams of paper were all the same price and the inkjet cartridges were all the same price. Write a system of equations, then solve.
24p + 4c = 320
2p + 1c = 50
p = $7.50
c = $35
Find the first five terms of each sequence:
a1 = -2, an = 4an-1 + 5, n > 2
-2, -3, -7, -23, -87
Find five consecutive odd integers from least to greatest in which the sum of the first and the fifth is one less than three times the fourth.
-9, -7, -5, -3, -1