1. Find equations of lines

2. Another way to write the equation of a line is:
General equation is:
y=mx+c
Another way to write the equation of a line is:
ax + by +c = 0

3. Today we are going find what you already know to find the equation of a line …
when you are given:
the gradient, m and
a point (x,y)

4. Find the equation of the line that passes through (2,3) with
m=3/4
It’s simple – because we know that the equation of a line is……
We are given m in the question so all we have to really do is find c
y=mx+c
We have to find m and c
What other info are we given that we haven’t used??

5. Find the equation of the line that passes through (2,3) with m=3/4
Then c is the only thing we don’t know so we can solve the equation to find it
Correct – the point (2,3) tells us that x=2 and y=3
So we sub:
m=3/4, x=2 and y=3 into
y=mx+c

6. Find the equation of the line that passes through (2,3) with m=3/4
y=mx+c
To find c: sub in m=3/4, x=2 y=3
3=3/4 x 2 + c
3=1.5 + c
c=1.5 or 3/2
So the equation of the line is:
y = 3/4x + 3/2

7. To be real posh we often remove fractions from equations
How could be remove fractions from:
y = 3/4x + 3/2
How could be remove fractions from:
y = 3/4x + 3/2
Multiply by 4 to every term:
Multiply by 4 to every term:
4y = 3x + 6
Now put in the form ax + by = 0:
-3x + 4y - 6 = 0
or remove the –ve from x by multiplying by -1
3x - 4y + 6 = 0
Now put in the form ax + by = 0:
-3x + 4y - 6 = 0
or remove the –ve from x by multiplying by -1
3x - 4y + 6 = 0

8. So to summarise:
Given the gradient m and a point (x,y) the equation of the line can be found by:
Step One – Find c by:
Sub m= and x= and y= into: y=mx+c
Step Two - Write the equation by subbing in m and c into: y=mx+c
(Rearrange only if required to)