This document provides instruction on writing the equation of a line given two points. It explains that you need to find the slope (m) using the slope formula, and the y-intercept (b) by substituting a point into the line equation y=mx+b. Several examples are worked through step-by-step to demonstrate this process. First the slope and one point are given, then students are asked to find the full equation. Finally, students are instructed to practice writing the full equation on their own given just two points on a line.

1. Skill31C Writing the equation of a line pages 167 and 168 in the book
The ultimate goal of this lesson is to be able to write an equation of a line given
two points on the line. We will do this in two phases starting with a given slope and
a point. This type of question is very likely to be on the test!
Here is the kind of problem we are talking about.
Write the equation of a line in slope-intercept form of a line passing through (2,3) and (4,7).
To answer this question, we need the slope, m, and the y-intercept, b, so that we can
Write the equation in the form y = mx + b. The answer is y = 2x -1. How?
First find the slope using the slope formula. (y2- y1)/ (x2 – x1)
Here that is (7-3)/(4-2) or 4/2 or just 2. So m = 2 Now we have y = 2x + b.
Now we have to find the b number and we are done. To find b, pick either of the original
ordered pairs (2,3) or (4,7). It doesn’t matter which one. We will get the same answer
either way. So pick the easiest looking one. (No negatives, easy numbers ==maybe a 0).
I will pick (2,3). That means let x = 2 and y = 3. Use those numbers along with the m = 2 we just
found. Now we have 3 = 2(2) + b or 3 = 4 + b or -1 = b
Now go back to the formula y = mx + b and replace m and b with the numbers
We found. Answer y = 2x - 1

2. Now to practice getting these figured out, we will start with a hint first.
I will give you the slope at first along with one point. After you practice this,
You will be ready to do the problems like the one on the first page.
If m = 3 and the line passes through (4,5), find the equation of the line.
We know y = 3x + b given that the slope is 3. Now let x = 4 and y = 5 in the equation to
Get 5 = 3(4) + b
5 = 12 + b
-12 -12
-7 = b
So the equation is y = 3x -7.
Try this one.
We know y = 2x + b
Then let x = 3 and y = 2 to get
2 = 2(3) + b
2 = 6 + b
-6 -6
-4 = b
So, y – 2x -4

3. Write y = -3x + b
Let x = 1 and y = 4 to get
4 = -3(1) + b
4 = -3 + b
+3 +3
7 = b
So y = -3 x + 7
Now we are ready for the kind of problem like you will see on the test.

4. Write the equation of a line passing through these points.
First we must find the slope ourselves. This is
the only step we add to the last problems.
Slope = (7 – 5) / (2 – 1) or 2/1 or 2
Now you pick the point you like (1,5) or (2,7).
I am picking (1,5) so that x = 1 and y = 5
Now write y = mx + b with the number we have.
5 = 2(1) + b
5 = 2 + b
-2 -2
3 = b
So now go back and write y = mx + b with our
m number and b number.
Y = 2 x + 3

5. Find the equation of the line passing through
Slope = ( -2 - -3)/ (4 – 2) or (-2 + 3)/ 2 or ½ Use 0.5 in the problem.
I am picking (2, -3) to write -3 = 0.5 (2) + b
-3 = 1 + b
-1 -1
-4 = b
So now y = mx + b becomes y = 0.5 x -4 or y = ½ x - 4
Remember that these problems are in the “calculator allowed” section of the test.
Use the calculator to help find the slope and any other part you need it.
Try some of the problems at the top of page 168. The ones at the bottom have too many
Harder parts.