Slope-intercept form

In the standard form y = mx + c, the coefficient of x gives the slope and the constant c gives the y-intercept. Comparing y = 13x - 6 with this form gives m = 13, which is positive, and c = -6, which is negative. Thus option A is correct. The other choices either reverse one sign or incorrectly claim that both signs are alike.

The governing concept is identifying slope after converting an equation to y = mx + c. Divide every term of 2y = (a - 4)x + 16 by 2: y = ((a - 4)/2)x + 8. Hence the coefficient of x, and therefore the slope, is (a - 4)/2. The given slope is 3, so (a - 4)/2 = 3. Multiplying both sides by 2 gives a - 4 = 6, and adding 4 gives a = 10. Thus option B is correct. Option A would result from mishandling the subtraction, while options C and D do not satisfy the equation. A frequent error is to call a - 4 the slope before dividing the entire equation by 2; the coefficient must be read only after y has been isolated.

To isolate y, subtract 14x from both sides: 7y = -14x + 35. Dividing every term by 7 gives y = -2x + 5. Comparing this with y = mx + c shows m = -2 and c = 5, so option A is correct. The other options result from failing to divide by 7 or from losing the negative sign.

First move the x-term to the other side: 4y = -16x + 52. Divide the complete equation by 4 to obtain y = -4x + 13. In y = mx + c, the x-coefficient is the slope and the constant is the y-intercept. Hence m = -4 and c = 13, making option A correct; the other choices omit division or mishandle signs.