y = mx + b needs the slope and the intercept. Point-slope needs the slope and any point.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Finding b
Substitute the known point into y = mx + b and solve for b. That is the whole trick.
From two points
Compute the slope first, then use either point to find b.
Check with the other point
A line through two points must satisfy both. Testing the unused one catches arithmetic slips.
From a point and a slope
Substitute directly into y − y₁ = m(x − x₁). With slope 3 through (2, 5): y − 5 = 3(x − 2). Expanding gives y = 3x − 1. Point-slope exists precisely so this case takes one substitution.
From two points
Compute the slope first, then use either point in point-slope form. Both points give the same final equation, so using the second one afterwards is a free check on your algebra.
From a graph
Read the y-intercept off the axis and count the rise and run between two clear lattice points for the slope. Choosing points that fall exactly on grid intersections avoids introducing reading errors.
Verify with the given points
Substitute each given point into your final equation and confirm it satisfies it. A line that misses one of the points it was built from has an arithmetic error, and this check finds it in seconds.
Step 2: Try It Yourself
Tap and try it out.
The slope is 3: for every 1 across, the line goes 3 up.
Step 3: Watch an Example
One step at a time.
Watch Priya Build a Line
Priya writes the line with slope 3 through (2, 11).
- Step 1
She starts from y = 3x + b.
Step 4: Your Turn
Practice makes it stick.
Finding b
Problem 1 of 2
Slope 2 through (3, 11). What is b?
Through the Origin
Problem 2 of 2
Slope 4 through (0, 0). What is b?
Build the Equation
1 of 8
Slope 5 through (1, 9). What is b?
2 of 8
Slope −2 through (3, 1). What is b?
3 of 8
Through (0, 5) and (2, 11). What is the slope?
4 of 8
Same two points. What is b?
5 of 8
y = 4x + 7. What is y at x = 2?
6 of 8
Order the steps for writing a line through two points.
- 1Substitute one point into y = mx + b
- 2Solve for b
- 3Check with the other point
- 4Compute the slope
7 of 8
Slope 0 through (4, 9). What is b?
8 of 8
Through (1, 4) and (3, 10). What is the slope?
Step 5: Quick Check
Show what you know.
Question 1 of 1
Slope 3 through (2, 10). What is b?
What You Learned
- y = mx + b needs a slope and an intercept.
- Substitute a known point to find b.
- From two points, find the slope first, then b, then check with the unused point.