Lines are in the form y=mx+b, where m is the slope and b is the y-intercept. This line is thus y=9/4x-14, so C is correct. Multiplying by four, we get 4y=9x-56. Adding 56 and subtracting 4y, we see that 9x-4y=56, and multiplying by -1, we get 4y-9x=-56, so A is also correct. At this point, it is clear that B and D are incorrect, so A and C only are correct.
You know that you can spot the slope and intercept right away IF you 'solve' the equation for 'y'. Then you'll have
y = (slope) x + (intercept) .
So for choices 'A' and 'B', you have to massage the equation into the standard form, and then just look at it and see whether the slope is 9/4 and the intercept is -14.
A). -9x + 4y = -56
Add 9x to each side: 4y = 9x - 56
Divide each side by 4 : y = 9/4 x - 14 <== Yes ! Good one.
B). 9x + 4y = 56
Subtract 9x from each side: 4y = -9x + 56
Divide each side by 4 : y = -9/4 + 14 <= no, signs are wrong
C). Yes. Slope is 9/4 and intercept is -14 .
D). No. Slope is 9/4 alright, but intercept is +14, not -14 .
