Cogito
Algebra 1 · Chapter 4 · Lesson 3
Writing the Equation of a Line
From a slope and a point, or from two points.
11 problems · about 23 minutes · A-CED.A.2, F-LE.A.2
What this lesson teaches
The student writes a linear equation from given information.
- 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.
Warm Up
Straightforward practice. Get the method working first.
4 problemsSlope 3 through (2, 10). What is b?
Answer 4
Why 4.
Slope 5 through (1, 9). What is b?
Answer 4
Why 9 = 5 + b.
Slope −2 through (3, 1). What is b?
Answer 7
Why 1 = −6 + b.
Through (0, 5) and (2, 11). What is the slope?
Answer 3
Why 6 ÷ 2.
Build It Up
The same ideas with more to keep track of.
3 problemsSame two points. What is b?
Answer 5
Why Read it off the first point.
y = 4x + 7. What is y at x = 2?
Answer 15
Why 8 + 7.
Order the steps for writing a line through two points.
Answer 1. Compute the slope 2. Substitute one point into y = mx + b 3. Solve for b 4. Check with the other point
Why The slope is needed before b can be found.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSlope 0 through (4, 9). What is b?
Answer 9
Why A horizontal line.
Through (1, 4) and (3, 10). What is the slope?
Answer 3
Why 6 ÷ 2.
Finding b: Slope 2 through (3, 11). What is b?
Answer 5
Why 5.
Through the Origin: Slope 4 through (0, 0). What is b?
Answer 0
Why 0.