Find equations of lines

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Presentation transcript:

Find equations of lines

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

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)

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??

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

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

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

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)