Expert: Ahmed Salami - 4/26/2007

Question
i wanted to see your answer for this please,and how you may re-arrange the equation to get y=mx+c, to use for the tablfor the graph.


Question

Determine the gradient and y-intercept of the lines.

(ii)

4x-3y=12

(iii)

5x+2y=20

many thanks

Answer
Hi Pearl,
The general form of the equation of a straight line is
y = mx   c
where m is the gradient and c is the y-intercept.
To re-arrange an equation of the ax   by   c = 0, we simply make y subject of the formula.
Now, going to your questions.
For 4x - 3y = 12
substracting 12 from both sides of the equation
4x - 3y - 12 = 12 - 12
4x - 3y - 12 = 0
adding 3y to both sides
4x - 3y - 12   3y = 3y
4x - 12 = 3y
dividing through by 3
(4x - 12)/3 = 3y/3
(4/3)x - 12/3 = 3y/3
(4/3)x - 4 = y
or simply
y = (4/3)x - 4
comparing with y = mx   c
m = 4/3 and c = -4

The other question can be solved in pretty much the same way
5x   2y = 20
5x - 20 = -2y
dividing through by -2
(5/-2)x - (20/-2) = (-2/-2)y
-(5/2)x - (-10) = y
-(5/2)x   10 = y
or simply
y = -(5/2)x   10
hence
m = -5/2 and c = 10

I hope i have helped you. You can always get back to me.
Regards.