Cogito
Integrated Math 1 · Chapter 2 · Lesson 2
Forms of a Linear Equation
Three ways to write the same line.
12 problems · about 21 minutes · A-CED.A.2, F-IF.C.7
What this lesson teaches
The student writes linear equations in slope-intercept, point-slope and standard form and converts between them.
- Slope-intercept form is y = mx + b, best for graphing.
- Point-slope form builds a line from any point and a slope.
- Standard form handles vertical lines, which slope-intercept cannot.
Warm Up
Straightforward practice. Get the method working first.
5 problemsSlope 2 through (3, 10), as y = 2x + b. What is b?
Answer 4
Why 4.
How do you convert any form to slope-intercept form?
Answer Solve the equation for y.
Why Isolate y.
y = 5x + 2. What is the slope?
Answer 5
Why The coefficient of x.
y = −2x + 8. What is the y-intercept?
Answer 8
Why The constant.
Slope 2 through (0, 5). What is b?
Answer 5
Why The point is already the intercept.
Build It Up
The same ideas with more to keep track of.
3 problemsSlope 4 through (1, 10), as y = 4x + b. What is b?
Answer 6
Why 10 = 4 + b.
2x + y = 7 solved for y gives y = −2x + c. What is c?
Answer 7
Why Subtract 2x from both sides.
Which form can describe a vertical line? 1 slope-intercept, 2 standard.
Answer 2
Why A vertical line has no slope.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsMatch each form with what it makes easiest.
Answer Slope-intercept form → Graphing straight from the equation; Point-slope form → Building a line from a point and a slope; Standard form → Handling vertical lines
Why Each form is convenient for a different task.
Slope −3 through (2, 1), as y = −3x + b. What is b?
Answer 7
Why 1 = −6 + b.
The Intercept: y = 4x − 9. What is the y-intercept?
Answer -9
Why −9.
The Line: Slope 3 through (2, 7), written as y = 3x + b. What is b?
Answer 1
Why 1.