Week 21: Writing the equation of a line

Field Book

75 to 78

Due

Test 18 due

Method

Paper first, every step

Up to now you have been handed equations and asked to draw them. This week it runs the other way: you are handed a line, or two facts about one, and asked to write its equation. Slope-intercept form is the whole toolkit. Once you can read m and b off a picture and write them into y = mx + b, lines stop being mysterious for good.

What you have to be able to do

Write y = mx + b from a slope and a y-intercept
Graph a line straight from slope-intercept form
Set up a consecutive integer problem and solve a rational equation

The procedures

Slope-intercept form

y = mx + b. The m is the slope and the b is where the line crosses the y axis.
To graph it, plot b on the y axis first. That is your starting point.
Then count the slope as rise over run from that point and mark a second one.

Consecutive integers

Call the first one n. The next ones are n + 1 and n + 2.
For consecutive odd or consecutive even, they go n, n + 2, n + 4. The gap is two either way.
Write the sentence as an equation, solve for n, then list all the numbers asked for.

Rational equations

Multiply every term on both sides by the LCD to clear the denominators.
Solve the equation that is left.
Check the answer against the original denominators. Anything that makes one zero is thrown out.

Worked

WORKED

Write the equation of a line with slope 3 crossing the y axis at −2.
m is 3 and b is −2. Drop them into y = mx + b.
ANSWER: y = 3x − 2

WORKED

Three consecutive integers add to 48. Find them.
n + (n + 1) + (n + 2) = 48, so 3n + 3 = 48.
3n = 45, so n = 15.
ANSWER: 15, 16, and 17

Terms

Term	Meaning
slope	rise over run, how steep the line is and which way it leans
y-intercept	where the line crosses the y axis, the b in y = mx + b
consecutive integers	whole numbers in a row, each one more than the last

Check yourself

1. Write the line with slope −2 and y-intercept 5

2. Two consecutive integers add to 27. Find them.

3. Solve x4 + 1 = 3

reveal answers

y = −2x + 5 · 13 and 14 · x = 8

This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.