Slope-intercept form: write an equation from a table
Key Notes:
Linear functions are of the form y = mx + b. In f(x) notation, this is the same as f(x) = mx + b.
Learn with an example
First, find m. Look at the table and notice that every time the x terms go up by 1, the y terms go up by 1. This means that m is equal to 1.
| x | y |
| 5 | 0 |
| 6 | 1 |
| 7 | 2 |
| 8 | 3 |
Next, find b. Take the equation y = mx + b and plug in the m value (m = 1) and a pair of (x, y) coordinates from the table, such as (5, 0). Then solve for b.
y = mx + b
0 = 1(5) + b Plug in m = 1, x = 5, and y = 0
0 = 5 + b Simplify
–5 = b Simplify
Finally, use the m and b values you found (m = 1 and b = -5) to write the equation.
y = mx + b
y = 1x + –5 Plugin m = 1 and b = –5
y = x − 5 Simplify
Now check your answer. Plug in each (x, y) pair in the table, and see if the result is a true statement.
Plug in (5, 0).
y = x − 5
0 = 5 – 5
0 = 0
Plug in (6, 1).
y = x − 5
1 = 6 – 5
1 = 1
Plug in (7, 2).
y = x − 5
2 = 7 – 5
2 = 2
Plug in (8, 3).
y = x − 5
3 = 8 – 5
3 = 3
Each (x, y) pair from the table resulted in a true statement.
So, the equation is y = x − 5. In f(x) notation, this is f(x) = x − 5.
Fill in the missing number to complete the linear equation that gives the rule for this table.
| x | f(x) |
| 3 | 18 |
| 4 | 24 |
| 5 | 30 |
| 6 | 36 |
f(x) = _____ x
First find m. Look at the table and notice that every time the x terms go up by 1, the y terms go up by 6. This means that m is equal to 6.
| x | y |
| 3 | 18 |
| 4 | 24 |
| 5 | 30 |
| 6 | 36 |
Next find b. Take the equation y = mx + b and plug in the m value (m = 6) and a pair of (x, y) coordinates from the table, such as (3, 18). Then solve for b.
y = mx + b
18 = 6(3) + b Plug in m = 6, x = 3, and y = 18
18 = 18 + b Simplify
0 = b Simplify
Finally, use the m and b values you found (m = 6 and b = 0) to write the equation.
y = mx + b
y = 6x + 0 Plug in m = 6 and b = 0
y = 6x Simplify
Now check your answer. Plug in each (x, y) pair in the table, and see if the result is a true statement.
Plug in (3, 18).
y = 6x
18 = 6(3)
18 = 18
Plug in (4, 24).
y = 6x
24 = 6(4)
24 = 24
Plug in (5, 30).
y = 6x
30 = 6(5)
30 = 30
Plug in (6, 36).
y = 6x
36 = 6(6)
36 = 36
Each (x, y) pair from the table resulted in a true statement.
So, the linear equation is y = 6x. In f(x) notation, this is f(x) = 6x.
Which equation gives the rule for this table?
| x | f(x) |
| 4 | 15 |
| 5 | 16 |
| 6 | 17 |
| 7 | 18 |
- f(x) = 5x + 11
- f(x) = –5x + 11
- f(x) = x + 11
- f(x) = –x + 11
First find m. Look at the table and notice that every time the x terms go up by 1, the y terms go up by 1. This means that m is equal to 1.
| x | y |
| 4 | 15 |
| 5 | 16 |
| 6 | 17 |
| 7 | 18 |
Next find b. Take the equation y = mx + b and plug in the m value (m = 1) and a pair of (x, y) coordinates from the table, such as (4, 15). Then solve for b.
y = mx + b
15 = 1(4) + b Plug in m = 1, x = 4, and y = 15
15 = 4 + b Simplify
11 = b Simplify
Finally, use the m and b values you found (m = 1 and b = 11) to write the equation.
y = mx + b
y = 1x + 11 Plug in m = 1 and b = 11
y = x + 11 Simplify
Now check your answer. Plug in each (x, y) pair in the table, and see if the result is a true statement.
Plug in (4, 15).
y = x + 11
15?4 + 11
15 = 15
Plug in (5, 16).
y = x + 11
16?5 + 11
16 = 16
Plug in (6, 17).
y = x + 11
17?6 + 11
17 = 17
Plug in (7, 18).
y = x + 11
18?7 + 11
18 = 18
Each (x, y) pair from the table resulted in a true statement.
So, the equation is y = x + 11. In f(x) notation, this is f(x) = x + 11.
Let’s Practice!
