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maths help please

the line y= 1/2x +6 meets x axis at point c. find the equation of the line with gradient 2/3 that passed through point c.

so x = -12

y -6 = 2/3 (x+12)
I x by 3 to get rid of fraction
3y-18=2x+24

now I have to put it in the form ax+by+c = 0

the answer is 2x-3y + 24
I got the 2x-3y but how do i get the 24?
thanks
Point C is where the Line y=1/2x+6 meets the x axis

You correctly rearranged to get x=-12, and since the x axis is where y=0, point C should be (-12,0)

However, when you substituted this into y-y1=m(x-x1), you stated the y value as 6, when it should be 0 as that is the y-coordinate of point C.

So you should get ---> y-0=2/3(x+12)

y=2/3x + 24/3

Multiply all values by 3 gives you--> 3y=2x+24

Then rearrange to get--> 2x-3y+24=0
Original post by DeclanCael
Point C is where the Line y=1/2x+6 meets the x axis

You correctly rearranged to get x=-12, and since the x axis is where y=0, point C should be (-12,0)

However, when you substituted this into y-y1=m(x-x1), you stated the y value as 6, when it should be 0 as that is the y-coordinate of point C.

So you should get ---> y-0=2/3(x+12)

y=2/3x + 24/3

Multiply all values by 3 gives you--> 3y=2x+24

Then rearrange to get--> 2x-3y+24=0


Ahh thanks!! I was putting +6 as the y coord because its the y intercept loool but thats not even the same equation
thanks :smile:
Original post by samantham999
Ahh thanks!! I was putting +6 as the y coord because its the y intercept loool but thats not even the same equation
thanks :smile:


No problem :smile:
Original post by DeclanCael
No problem :smile:


for y=-2x +8 meets y axis at point b, find equation of line with gradient 2 passes through point B

So I got y=2x-8 but it says y=2x+8 :frown:
Original post by samantham999
for y=-2x +8 meets y axis at point b, find equation of line with gradient 2 passes through point B

So I got y=2x-8 but it says y=2x+8 :frown:


Point B is the y intercept, which you can get from the equation of the line as 8.

The y intercept is when x=0, so Point B is at (0,8)

Try putting this into the equation y-y1=m(x-x1) again, make sure you don't get your x's and y's mixed up.
Original post by DeclanCael
Point B is the y intercept, which you can get from the equation of the line as 8.

The y intercept is when x=0, so Point B is at (0,8)

Try putting this into the equation y-y1=m(x-x1) again, make sure you don't get your x's and y's mixed up.


I keep getting this y-8= 2(x-4)
y-8=2x-8
:/
Original post by samantham999
I keep getting this y-8= 2(x-4)
y-8=2x-8
:/


The left side of your answer is correct, so you are using the correct value for y. On the right side, you have the right gradient but not the correct x value.

Remember that point B is (0,8) as we said before.

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