Slope and y-intercept

Correct answer: A. Slope positive and y-intercept negative

Compare y = 11x - 4 with y = mx + b. The coefficient of x is m = 11, which is positive, so the slope is positive. The constant term is b = -4, which is negative, so the y-intercept is negative. Therefore option A is correct. The signs must be read separately; the positive coefficient does not make the constant positive, and the negative constant does not change the slope.

Correct answer: A. 11

The governing concept is point substitution in the slope-intercept equation y = mx + b. Every point on a line must satisfy its equation. Substitute x = 5 and y = -4 into y = -3x + b: -4 = -3(5) + b = -15 + b. Add 15 to both sides to isolate the unknown constant: b = -4 + 15 = 11. Therefore, option A is correct. The value b is also the y-intercept because it is the constant term in the equation. Option B can arise from an addition or sign error, option C incorrectly combines the negative terms, and option D fails because -3(5) + 15 equals 0, not -4. Substitution directly verifies the answer.