Question

Select the correct graph of -4x + 3y = 6.

Answer 1

The easiest way to work out the answer is to work it out.

If x = 0
-4 X 0 = 0.
6 - 0 = 6. 6 / 3 = 2.
If x = 0, y = 2

If x = 1.
-4 X 1 = -4.
6 - -4 = 6 + 4 = 10.
10 / 3 = 3.33333

If x = 2
-4 X 2 = -8
6 - -8 = 6 + 8 = 14
14 / 3 = 4.666666

Now that you've got 3 of the answers, you check your graphs to see which one fits.
The answer is the first graph.

Answer 2

-4x + 3y = 6.

Rearrange into form y = mx + c.
3y = 4x + 6. Divide by 3.
y = (4/3)x + 2.

Therefore slope, m = (4/3), Y Intercept, c = 2.
X intercept, that is when y = 0.
y = (4/3)x + 2.
0 = (4/3)x + 2.
-(4/3)x = 2.
x = (2*3)/-4 = -3/2 = -1.5. X intercept is = -1.5.

Looking at the pictures, and using y and x intercepts as 2 and -1.5 respectively.
Also note that the slope is positive (4/3) so line climbs upwards from left to right.
Answer =
Graph (a). Cheers.