Writing Linear Equations
A linear equation describes the relationship between the x-coordinate and y-coordinate in the
ordered pairs making up a line.
To write a linear equation, two pieces of information are needed:
1. Slope
2. Y – intercept
Part 1: Positive Slope
Find the equation of the line that passes through the ordered pairs (-2, -1) and (1, 5).
Step 1: Find the slope
3
x
y
-2
-1
1
5
6
1. Write the given ordered pairs in a table.
2. Find the distance between the y-values.
3. Find the distance between the x-values.
Moving from -1 to 5 on a number
line, I move 6 units to the right.
Moving from -2 to 1 on a number
line, I move 3 units to the right.
change in y
4. Slope can be found using the following: change in x
In this case, this would be 6. The slope is 2.
3
Step2: Find the y-intercept
In the slope-intercept form, y = mx + b, the y-intercept is the value being added or subtracted.
1. Choose one of the given ordered pairs.
2. Multiply the slope by the x-coordinate.
3. Does the answer in step 2 equal the y-coordinate in
the chosen ordered pair?
4. What value needs to be added or subtracted to get to
the y-coordinate?
(-2, -1)
The slope is 2; the x-coordinate is -2, so
2 x -2 = -4
No. The given y-coordinate is -2;
however, the answer in step 2 is -4.
We are at -4. To get to -1 move 3 to the
right or add 3. The y-intercept is 3.
Therefore, the equation of the line which passes through (-2, -1) and (1, 5) is y = 2x + 3.
Part 2: Negative Slope
Find the equation of the line that passes through the ordered pairs (3, -5) and (-1, 7).
Step 1: Find the slope
-4
x
y
3
-5
-1
7
12
1. Write the given ordered pairs in a table.
2. Find the distance between the y-values.
3. Find the distance between the x-values.
Moving from -5 to 7 on a number
line, I move 12 units to the right.
Moving from 3 to -1 on a number
line, I move 4 units to the left, so I
write -4.
change in y
5. Slope can be found using the following: change in x
In this case, this would be 12. The slope is -3.
-4
Step2: Find the y-intercept
In the slope-intercept form, y = mx + b, the y-intercept is the value being added or subtracted.
1. Choose one of the given ordered pairs.
2. Multiply the slope by the x-coordinate.
3. Does the answer in step 2 equal the y-coordinate in
the chosen ordered pair?
4. What value needs to be added or subtracted to get to
the y-coordinate?
(3, -5)
The slope is -3; the x-coordinate is 3, so
-3 x 3 = -9
No. The given y-coordinate is -5;
however, the answer in step 2 is -9.
We are at -9. To get to -5 move 4 to the
right or add 4. The y-intercept is 4.
Therefore, the equation of the line which passes through (3, -5) and (-1, 7) is y = -3x + 4.
Part 2: Negative Slope and Negative Y-intercept
Find the equation of the line that passes through the ordered pairs (-2, 1) and (3, -9).
Step 1: Find the slope
5
x
y
-2
1
3
-9
-10
1. Write the given ordered pairs in a table.
2. Find the distance between the y-values.
3. Find the distance between the x-values.
Moving from 1 to -9, I move 10 to
the left, so I write -10.
Moving from -2 to 3, I move 5
units to the right.
change in y
6. Slope can be found using the following: change in x
In this case, this would be -10. The slope is -2.
5
Step2: Find the y-intercept
In the slope-intercept form, y = mx + b, the y-intercept is the value being added or subtracted.
1. Choose one of the given ordered pairs.
2. Multiply the slope by the x-coordinate.
3. Does the answer in step 2 equal the y-coordinate in
the chosen ordered pair?
4. What value needs to be added or subtracted to get to
the y-coordinate?
(3, -9)
The slope is -2; the x-coordinate is 3, so
-2 x 3 = -6
No. The given y-coordinate is -9;
however, the answer in step 2 is -6.
We are at -6. To get to -9 move 3 to the
left or subtract 3. The y-intercept is
-3.
Therefore, the equation of the line which passes through (-2, 1) and (3, -9) is y = -2x - 3.