Higher Maths - Straight Line Question

[jodyemm]

Find the equation of the straight line which is parallel to the line with equation 2x+3y=5 and which passes through the points (2,-1)

[Buenchico]

If you need to ask this many questions here, you really need to talk to your maths teacher to get some help!

You should know that y= mx + c is the equation of a straight line with a gradient of m and a y-intercept of c.
Let's rearrange 2x = 3y = 5 into that form:
2x + 3y = 5
<=>
3y = -2x + 5
<=>
y = -2/3 x + 5/3

So we know that the line in the question must have a gradient of -2/3
Any line which is parallel to it must also have the same gradient.

So we're seeking a line with an equation in the form y = mx + c
where m = -2/3
and where x=2 and y = -1 (from the coordinates in the question) satisfy that equation.

That gives us
-1 = (-2/3 times 2) + c
Adding 4/3 to both sides of the equation gives
c = 1/3

So the equation we require is y = -2/3 x + 1/3
To tidy that up, multiply throughout by 3:
3y = -2x +1
and then add 2x to both sides:
2x + 3y =1

Chris

[starone]

Chris you are a genius.You lost me on the first line.