Coordinate geometry

Are you asked to choose only one of the four choices, or is this one in which you may select multiple answers? Envisioning potential positive slopes for this line, it appears to me that the slope will be positive if c < 7. So choice a, c>0, is not always true. But it may be true sometimes (if 0 < c < 7), and choices b and c will always be true.

Choice d, none of the above, may also be the only correct answer if the answer being sought is which of the first three choices is the only one that is always true.

No, there is one and only one answer . but how c is not greater than 0 ?

c can be less than or equal to zero depending on where the line containing the point (5,7) intersections the y axis (the y-intercept).

An example of when c = 0 is 7x - 5y = 0 -> y = (7/5) x (slope = 7/5, c = 0)

An example of when c < 0 is 8x - 5y = 5 -> y = (8/5) x - 1 (slope = 8/5, c = -1)

An example of when c > 0 and slope is positive is x - y = -2 -> y = x + 2 (slope = 1, c = 2)

An example of when c > 0 and slope is negative is x + y = 12 -> y = -x + 12 (slope = -1, c = 12)

The only case of when c > 0 and slope is zero is y = 7 (c = 7)

More simply stated:

When 0 < slope < 7/5, c > 0

When slope = 7/5, c = 0

When slope > 7/5 c < 0

When c < 0, slope > 7/5

When c = 0, slope = 7/5

When c > 0, slope < 7/5, which means the slope can be negative.

But in question, l has positive slope is only given