Worked examples
The question
Question: write 2x + y = 5 as y = mx + b.
2x + y = 5
We want y by itself.
Then we can read m and b.
y = mx + b
1 Remove the 2x
We want y by itself.
The 2x is in the way.
To remove 2x, we take away 2x.
We do it on both sides, so they stay equal.
2x + y − 2x = 5 − 2x
2x and − 2x make zero.
Cross them out.
Write what is left.
5 and − 2x are not like terms.
They stay as they are.
y = 5 − 2x
We write the x part first, like in y = mx + b.
Each part keeps its sign.
y is by itself.
y = −2x + 5
2 Read m and b
m is the number in front of x: −2.
It is the slope.
m = −2
slope
b is the number on its own: 5.
The line crosses the y-axis at 5.
That point is called the y-intercept.
b = 5
crosses the y-axis
3 Check
Let's check with a point.
Put x = 2 into y = −2x + 5.
We get y = 1.
y = −2(2) + 5 = −4 + 5 = 1
Now put x = 2 and y = 1 into 2x + y.
2(2) + 1 = 4 + 1 = 5
We get 5, the same as the right side.
So the new equation is right!
Let's look back.
First: remove the 2x.
Then: read m and b.
Last: check.
▶ Watch it solved
The question
Question: write 2x + 3y = 6 as y = mx + b.
2x + 3y = 6
We want y by itself.
Then we can read m and b.
y = mx + b
1 Remove the 2x
We want y by itself.
The 2x is in the way.
To remove 2x, we take away 2x.
We do it on both sides, so they stay equal.
2x + 3y − 2x = 6 − 2x
2x and − 2x make zero.
Cross them out.
Write what is left.
6 and − 2x are not like terms.
They stay as they are.
3y = 6 − 2x
We write the x part first, like in y = mx + b.
Each part keeps its sign.
3y = −2x + 6
2 Remove the 3
3y means 3 times y.
We want just y.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3y3 = −2x + 63
3 divided by 3 is 1.
So just y is left.
The 3 divides the whole right side.
So it divides every part: −2x and 6.
Each part keeps its sign on top.
y = −2x3 + 63
Careful!
Divide every part by 3, not only the number.
−2x must be divided by 3 too.
Careful: not y = −2x + 2 ✗
Minus over plus is minus.
−2x/3 is the same as −2/3 times x.
−2x3 = −23x
6 divided by 3 is 2.
63 = 2
So y = −(2/3)x + 2.
y = −23x + 2
3 Read m and b
m is the number in front of x: −2/3.
It is the slope.
m = −23
slope
b is the number on its own: 2.
The line crosses the y-axis at 2.
That point is called the y-intercept.
b = 2
crosses the y-axis
4 Check
Let's check with a point.
Put x = −3 into y = −(2/3)x + 2.
We get y = 4.
y = −23(−3) + 2 = 2 + 2 = 4
Now put x = −3 and y = 4 into 2x + 3y.
2(−3) + 3(4) = −6 + 12 = 6
We get 6, the same as the right side.
So the new equation is right!
Let's look back.
First: remove the 2x.
Then: remove the 3.
Then: read m and b.
Last: check.
▶ Watch it solved
The question
Question: write 3y − 2x = 6 as y = mx + b.
3y − 2x = 6
We want y by itself.
Then we can read m and b.
y = mx + b
1 Remove the − 2x
We want y by itself.
The − 2x is in the way.
To remove − 2x, we add 2x.
We do it on both sides, so they stay equal.
3y − 2x + 2x = 6 + 2x
− 2x and + 2x make zero.
Cross them out.
Write what is left.
6 and + 2x are not like terms.
They stay as they are.
3y = 6 + 2x
We write the x part first, like in y = mx + b.
Each part keeps its sign.
3y = 2x + 6
2 Remove the 3
3y means 3 times y.
We want just y.
To remove times 3, we divide by 3.
We do it on both sides, so they stay equal.
3y3 = 2x + 63
3 divided by 3 is 1.
So just y is left.
The 3 divides the whole right side.
So it divides every part: 2x and 6.
Each part keeps its sign on top.
y = 2x3 + 63
Careful!
Divide every part by 3, not only the number.
2x must be divided by 3 too.
Careful: not y = 2x + 2 ✗
2x/3 is the same as 2/3 times x.
2x3 = 23x
6 divided by 3 is 2.
63 = 2
So y = (2/3)x + 2.
y = 23x + 2
3 Read m and b
m is the number in front of x: 2/3.
It is the slope.
m = 23
slope
b is the number on its own: 2.
The line crosses the y-axis at 2.
That point is called the y-intercept.
b = 2
crosses the y-axis
4 Check
Let's check with a point.
Put x = 3 into y = (2/3)x + 2.
We get y = 4.
y = 23(3) + 2 = 2 + 2 = 4
Now put x = 3 and y = 4 into 3y − 2x.
3(4) − 2(3) = 12 − 6 = 6
We get 6, the same as the right side.
So the new equation is right!
Let's look back.
First: remove the − 2x.
Then: remove the 3.
Then: read m and b.
Last: check.
▶ Watch it solved
