Worked examples
The question
Question: write the equation for this table: x is 0, 1, 2, 3, and y is 5, 8, 11, 14.
x: 0, 1, 2, 3; y: 5, 8, 11, 14
We write it as a table.
1 Rate of change
Rate of change means: how much y changes when x goes up by 1.
y changes by 3 when x goes up by 1.
Change in y on top.
Change in x at the bottom.
= m = 31
m = change in y ÷ change in x
2 Start value
The start value is y when x is 0.
The table has x = 0: y is 5.
= b = 5
3 Write the equation
A line is y = m x plus b: m is the rate of change, b is the start value.
y = mx + b
So the equation is y = 3x + 5.
= y = 3x + 5
4 Check
Let's check with the last pair: x = 3.
The equation gives 14.
The table says 14.
So the answer is right!
x = 3: 3 × 3 + 5 = 14
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
▶ Watch it solved
The question
Question: write the equation for this table: x is 1, 2, 3, 4, and y is 7, 9, 11, 13.
x: 1, 2, 3, 4; y: 7, 9, 11, 13
We write it as a table.
1 Rate of change
Rate of change means: how much y changes when x goes up by 1.
y changes by 2 when x goes up by 1.
Change in y on top.
Change in x at the bottom.
= m = 21
m = change in y ÷ change in x
2 Start value
The start value is y when x is 0.
The table starts at x = 1.
We go back one step to x = 0: take away 2.
y at 0 is 5.
= b = 7 − 2 = 5
Careful!
7 is y at x = 1.
The start value is y at x = 0.
Careful: not b = 7 ✗
3 Write the equation
A line is y = m x plus b: m is the rate of change, b is the start value.
y = mx + b
So the equation is y = 2x + 5.
= y = 2x + 5
4 Check
Let's check with the last pair: x = 4.
The equation gives 13.
The table says 13.
So the answer is right!
x = 4: 2 × 4 + 5 = 13
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
▶ Watch it solved
The question
Question: write the equation for this table: x is 0, 3, 6, 9, and y is 1, 3, 5, 7.
x: 0, 3, 6, 9; y: 1, 3, 5, 7
We write it as a table.
1 Rate of change
Rate of change means: how much y changes when x goes up by 1.
y changes by 2 when x goes up by 3.
Change in y on top.
Change in x at the bottom.
That is 2/3 for each 1 of x.
= m = 23 = 23
m = change in y ÷ change in x
Careful!
x goes up by 3, not 1.
So we divide the change of y by 3.
Careful: not m = 2 ✗
2 Start value
The start value is y when x is 0.
The table has x = 0: y is 1.
= b = 1
3 Write the equation
A line is y = m x plus b: m is the rate of change, b is the start value.
y = mx + b
So the equation is y = 2/3x + 1.
= y = 23x + 1
4 Check
Let's check with the last pair: x = 9.
The equation gives 7.
The table says 7.
So the answer is right!
x = 9: 2/3 × 9 + 1 = 7
Let's look back.
First: rate of change.
Then: start value.
Then: write the equation.
Last: check.
▶ Watch it solved
