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Stage 8 · Algebra Stretch Skills
Equation of a Line from Two Points
Given two points, write the line's equation in y = mx + b form. You already know every piece — this lesson just puts them together into one organized, calculator-friendly process.
This stage contains advanced algebra skills that build on earlier lessons. You should already feel comfortable with slope and y = mx + b before starting this page. This lesson combines several earlier line skills together into one advanced algebra process.
You already know every part of this process. You know how to find slope from two points. You know what y = mx + b means. You know how to solve a small equation. All this lesson does is line those skills up in order. Now we combine earlier line skills together — slowly, one step at a time.
The hard part is the setup, not the arithmetic. Stay organized, write one substitution step at a time, and use the calculator for the numbers. Organization matters more than mental math here.
The 4-Step GED Workflow
Every "equation from two points" problem uses the same four steps. Learn this one routine and use it every single time — there is no second method to keep track of.
1
Find the slope from the two points. This is exactly the Finding Slope skill — change in y over change in x. The calculator is encouraged.
2
Substitute the slope and ONE point into y = mx + b. Pick either point — just make sure the x and y come from the same point. Label the values if it helps.
3
Solve for b. Do the arithmetic on the right side first, then move it across to get b alone.
4
Write the final equation. Drop your slope (m) and your starting value (b) back into y = mx + b.
m = y₂ − y₁x₂ − x₁ → y = mx + b
What the two letters mean. Slope tells how fast — how much y changes for every step right. b tells where the line starts — its value when x = 0. Keep that meaning in mind and the algebra stays connected to something real.
🔢 Worked Examples
Notice the same four steps repeat in every example. The numbers change; the routine never does.
slope (m) · x-value · y-value — colors track where each number comes from.
Example 1 — Basic Integer Slope
Find the equation of the line through (1, 3) and (5, 11).
→ Step 2 & 3 — The cost at month 0 is the starting value, so b = 25. (No need to solve — x = 0 hands you b directly.)
→ Step 4 — Slope is the monthly rate; b is the starting fee.
y = 10x + 25
⚠️ Common Mistakes
Almost every wrong answer on this skill comes from one of these. Knowing them in advance is half the battle — the Guided Practice bank includes "What mistake did the student make?" questions to train your eye.
Mixing up x and y
A point is (x, y) — first number x, second number y. Putting the y-values on the bottom of the slope formula flips the answer.
Coordinates from different points
The top of the slope formula uses both y-values; the bottom uses both x-values. Don't grab one number from each point in the wrong slot.
Lost negative signs
Subtracting a negative becomes adding: 4 − (−2) = 4 + 2 = 6. Write it out — don't do it in your head.
Forgetting to solve for b
Finding the slope is only Step 1. You still have to substitute a point and solve for b before you can write the equation.
Arithmetic on the wrong side
In 3 = 2(1) + b, finish the right side (2 × 1) before moving anything across. Use the calculator to avoid slips.
Wrong final format
The answer is y = mx + b: slope in front of x, b added at the end. Don't swap m and b or drop the "y =".
🎯 The whole process on one screen
1Slope: m = y₂ − y₁x₂ − x₁. Calculator welcome.
2Substitute: put m and one point's x and y into y = mx + b.
3Solve for b: finish the right side, then subtract to isolate b.
4Write it: y = mx + b with your slope and your b.
Reference
GED Formula Sheet
Both m = y₂ − y₁x₂ − x₁ and y = mx + b are given to you on test day.