💡 What You Will Learn
Given a slope (m) and a point (x₁, y₁) on a line, you can write the equation of that line. This is a common GED algebra topic. The key is knowing how to apply the point-slope formula and convert it to slope-intercept form (y = mx + b).
Use this to set up the equation when you're given m and a point. It's your starting tool.
This is the final form the GED expects. Solve for y to get y = mx + b.
Point-Slope → plug in m, x₁, y₁ → distribute → isolate y → Slope-Intercept ✅
The slope tells you how much y changes for every 1 unit x increases. It can be positive, negative, a fraction, or zero.
Examples: m = 2, m = −3, m = 2/3, m = −1/2
The y-intercept is the value of y when x = 0. It's the constant at the end of the equation.
Examples: y = 2x + 7, y = −3x + 11, y = (2/3)x − 1
This is the known point. Plug it into the point-slope formula. Be careful with negative values — always use parentheses: (−6) not just −6!
| Equation | m (slope) | b (y-intercept) |
|---|---|---|
| y = 2x + 5 | 2 | 5 |
| y = −3x + 11 | −3 | 11 |
| y = (2/3)x + 7 | 2/3 | 7 |
| y = (1/2)x − 1 | 1/2 | −1 |
y − y₁ = m(x − x₁)
Replace m with the given slope. Replace x₁ and y₁ with the given point. Watch your signs — negative values need parentheses!
Multiply m by both terms inside: m(x − x₁) = mx − m·x₁
Move the y₁ term to the right side to get y = mx + b. This is your final answer!
Trap 1: x₁ is negative → the formula becomes x − (−6) = x + 6
Trap 2: y₁ is negative → y − (−2) = y + 2
Trap 3: Distributing a negative slope — signs flip!
| Step | Action | Example (m=2/3, point (−6,3)) |
|---|---|---|
| 1 | Write formula | y − y₁ = m(x − x₁) |
| 2 | Plug in | y − 3 = (2/3)(x − (−6)) |
| 3 | Simplify & Distribute | y − 3 = (2/3)x + 4 |
| 4 | Isolate y | y = (2/3)x + 7 ✅ |
y − 3 = (2/3)(x − (−6))
y − 3 = (2/3)(x + 6)
y − 3 = (2/3)x + 4
y = (2/3)x + 7
When x₁ is negative (−6), the formula has x − (−6) which becomes x + 6. Two negatives make a positive — this is where most mistakes happen!
y − 5 = −3(x − 2)
y − 5 = −3x + 6
y = −3x + 11
y = (3/4)x + 3
y − (−2) = −(1/2)(x − 6)
y + 2 = −(1/2)(x − 6)
y + 2 = −(1/2)x + 3
y = −(1/2)x + 1
y − (−2) becomes y + 2 (left side). And −(1/2)·(−6) becomes +3 (right side). Two separate sign traps in one problem — write each step out!