What is the gradient and y intercept of these lines?

Question

2y=8x-6


3y+x=9

Could someone please explain how to work them out too.
I'm soo confused.
Thanks

Oh thank-you everyone! You have helped soo much! I understand it :D

Answer 1

Make y the subject of formula. The gradient is the coefficient of x.

2y=8x-6 (divide by 2 everywhere)
y=4x-3
Grad=4

3y+x=9 (make y subject)
3y=9-x (divide by 3 everywhere)
y=3-1/3x
Grad=-1/3

Answer 2

If you get your equation into the form y = mx + c then m is the gradient and c is the y-intercept of the line.

2y = 8x – 6
y = 4x – 3 (divide by 2)
So gradient is 4 and y-intercept is –3

3y + x = 9
y + x/3 = 3 (divide by 3)
y = –x/3 + 3 (subtract x/3 from both sides)
So gradient is –1/3 and y-intercept is 3.

Works every time!

Answer 3

one way of doing it is making y the subject so the line is in the form y=mx+b

this way you can immediately identify the gradient (which will be m) and the y-intercept (which is b)

2y=8x-6. rearraging to make y the subject..

y= (8x-6)/2 ====> y=4x-3

.: gradient is the coefficient of x which is 4
y intercept is -3

3y+x=9. making y the subject-

y= (9-x)/3 ===> y= 3-x/3
.: gradient is -1/3 (because there is a minus infront of the x)
y intercept is 3

Answer 4

2y=8x-6
y=4x-3------(dividing 2 at both side)
by comparing with y=mx+c
gradient=m=4
y intercept =c=-3


3y+x=9
3y=-x+9
y=-(1/3)x+3----------(dividing 3 to both side)
by comparing with y=mx+c
gradient=m=-1/3
y intercept =c=3

Answer 5

Line 1
y = 4x - 3
m = 4 is gradient
y = - 3 is intercept

Line 2
3y = - x + 9
y = (- 1/3).x + 3
m = (- 1/3) is gradient
y = 3 is intercept