Cogito
Algebra 1 · Chapter 4 · Lesson 1
Forms of a Linear Equation
Three ways to write the same line.
10 problems · about 20 minutes · F-IF.B.4, F-LE.A.2, A-CED.A.2
What this lesson teaches
The student writes linear equations in slope-intercept, point-slope, and standard form and converts between them.
- Slope-intercept form shows the slope and the crossing point.
- Point-slope form is for a known point and slope.
- Parallel slopes are equal; perpendicular slopes multiply to −1.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Piecewise Functions: f(x) = 5x for x < 2, else x + 50. What is f(1)?
Answer 5
Why 5.
Review — Rate of Change: From 5 to 25 over 4 steps. Rate?
Answer 5
Why 5.
Warm Up
Straightforward practice. Get the method working first.
4 problemsThrough (1, 2) and (4, 11). What is the slope?
Answer 3
Why 3.
What do perpendicular slopes multiply to?
Answer -1
Why −1.
Through (0, 5) with slope 3. What is b?
Answer 5
Why It crosses at 5.
Through (2, 7) and (4, 13). What is the slope?
Answer 3
Why 6 ÷ 2.
Build It Up
The same ideas with more to keep track of.
2 problemsy = 5x + 2. What is the slope of a parallel line?
Answer 5
Why Parallel means equal slopes.
y = 3x − 1. What is y when x = 4?
Answer 11
Why 12 − 1.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Slope: A line passes through (1, 4) and (5, 16). What is its slope?
Answer 3
Why 3.
Perpendicular: A line has slope 4. What is the slope of a perpendicular line, as the bottom number of a negative fraction with top 1?
Answer 4
Why −1/4.