Solving for x
Solve for x:
2x + 5 = 15
x = 5
3x + 5 = 3x - 2
No solution
Identify the slope (m) and y-intercept (b) of
y = 2x + 3
m = 2
b = 3
A gym membership costs $10 per month plus a $50 signup fee. Write an equation for the total cost (C) after x months.
C = 10x + 50
What is the slope of a horizontal line?
m = 0
Solve for x:
3(x - 4) = 18
x = 10
4x - 2 = 2x + 10
One Solution
x = 6
Graph y = -x + 4 and describe its slope.
A line with the slope of -1
You rent a car for $25 plus $0.10 per mile. Write and graph the equation. (Use whole numbers for your graph)
C = 0.10x + 25
(See slides for graph)
Find the x-intercept of
y = 2x - 8
x = 4
5x - 2 = 3x +10
x = 6
5x - 5 = 5(x - 1)
Infinitely many solutions
What is the equation of a line with a slope of 3 and a y-intercept of -2?
y = 3x - 2
A cellphone plan costs $20 per month plus $0.05 per text message. If you spend $35 in one month, how many texts did you send?
300 texts
What type of solution does 4(x - 1) = 4x - 4 have?
Infinitely many solutions.
Solve for x:
2(3x - 1) = 4x + 8
x = 5
2(x + 3) - x = x + 6
Infinitely many
Convert 3x + 4y = 12 into slope-intercept form.
y = -(3/4)x + 3
A store is having a sale: the price of a jacket is reduced by $5 every day. If the starting price was $60, write an equation that models the price over time (P).
P = 60 - 5x
Write an equation of a line parallel to y = -2x + 3 passing through (4,1).
y = -2x + 9
Solve for x:
(x/2) +4 = (3x/4) - 2
x = 24
Explain how to determine the number of solutions without solving the equation.
1. Rewrite the equation in standard form (Ax + B = C) if needed.
2. Compare the coefficients of x and the constants:
- Identical sides of equations = infinitely many solutions.
- Same coefficients of x but different constants = no solution.
- Different coefficients of x = one solution.
Two points on a line are (2,5) and (6,9). Find the slope and equation of the line.
y = x + 3
A business makes $500 per day in revenue but has $1,200 in daily costs. At what point does the business break even?
The company never breaks even.
A line has a slope of -3 and passes through (5,2). Write its equation in point-slope form.
y - 2 = -3(x - 5)