Solving Equations
Solve: x + 9 = 14
x = 5
What is the y-intercept of y = 3x + 4?
4 (the point (0, 4))
For the cost model y = 5x + 20, where x is hours and y is total cost in dollars, what does the 20 represent?
A fixed/starting cost of $20
"A number doubled, plus 3, equals 15." Write and solve the equation.
2x + 3 = 15, so x = 6
Simplify: 3x + 5x
8x
4x − 5 = 19
x = 6
What is the gradient of y = −2x + 5?
−2
In the equation, y = 5x + 20, where x is hours worked and y is the cost in dollars, what does the 5 represent?
A rate of $5 per hour
A phone plan costs $30 plus $0.50 per extra GB. Write a cost equation and find the cost for 10 extra GB.
C = 30 + 0.5g; C = $35
Substitute x = 4 into 2x + 7.
15
Solve: 3(x − 2) = 15
x = 7
A line passes through (0, 3) and has a gradient of 2. Write its equation.
y = 2x + 3
A taxi charges a $4 flag-fall plus $2 per km. Write an equation for cost, C, in terms of distance, d.
C = 2d + 4
A rectangle's perimeter is 36 cm and its length is 4 cm more than its width. Find the width.
w = 7 cm (length = 11 cm)
Which quadrant is the point (−3, 5) in?
Quadrant II (top-left)
Solve: 5x + 3 = 2x + 18
x = 5
Find the x-intercept of y = 2x − 8.
4 (the point (4, 0))
A plumber charges according to C = 60 + 45h. What is the call-out fee and the hourly rate?
$60 call-out fee, $45 per hour
Plan A costs a flat $10. Plan B costs $0.05 per message with no flat fee. How many messages make the plans cost the same?
200 messages
Simplify: 4(x + 2) − 3x
x + 8
Solve: (2x + 1) / 3 = 7
x = 10
A line has a gradient of ½ and passes through (4, 1). Find its equation.
y = ½x − 1
A 500 L tank drains at 25 L per minute. Write an equation for the volume V after t minutes, then find how long until it's empty.
V = 500 − 25t; empty after 20 minutes
One car rental charges $50 plus $0.20/km. Another charges a flat $90 with unlimited km. Find the breakeven distance.
200 km
Find the gradient between the points (1, 2) and (5, 10).
2 (rise 8 ÷ run 4)