Solving Equations
Solve: x + 7 = 15
x = 8
Graph: x > 5
Any number greater than 5
What does slope represent?
Rate of change
Write the equation of a line with slope 3 and y‑intercept −2.
y = 3x − 2
Solve: ∣x − 6∣ = 2
x = 8 or x = 4
Solve: 5x − 7 = 18
x = 5
What happens to the inequality sign when you multiply or divide both sides of an inequality by a negative number?
You flip the inequality sign to keep it true
What does the y‑intercept represent?
Starting value
Write an equation for a line passing through (1,5) with slope 2.
y = 2x + 3
How many solutions does ∣x∣ = −3 have?
No solutions
Solve: 3x + 4 = 2x + 11
x = 7
Solve: −3x < 12
x > −4
(flip the sign)
Identify the slope of:
y = −3x + 5
m = −3
Convert to slope‑intercept form:
y − 4 = −2(x + 1)
y = −2x + 2
What is the vertex of y = |x - 2| + 3?
(2, 3)
Solve: 4(2x − 3) = 20
x = 4
Solve and graph: 2x − 1 ≤ 5
x ≤ 3
Describe the slope in this situation:
“A car travels 60 miles per hour.”
The car travels 60 miles each hour
m = 60
Write an equation from the table: (1,4), (2,7), (3,10)
y = 3x + 1
Solve the system: y = x + 3
2x + y = 9
(2,5)
A gym charges a $20 signup fee and $10 per month. If the total cost is $80, how many months did the person attend?
6 months
Solve the compound inequality: −4 ≤ x + 2 ≤ 6
−6 ≤ x ≤ 4
Which line increases faster:
y = 2x + 1 or y = 5x − 4
y = 5x − 4
A phone plan costs $30 per month plus $5 per gigabyte. Write an equation for the total cost.
y = 30x + 5
How many solutions does the system have?
y = 2x + 1
y = 2x − 3
No solutions