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.

First rewrite the equation in slope-intercept form by dividing every term by 2: y = ((a - 4)/2)x + 8. Comparing this with y = mx + c shows that the slope is m = (a - 4)/2. The question states that the slope is 3, so (a - 4)/2 = 3. Multiplying by 2 gives a - 4 = 6, and adding 4 gives a = 10. Therefore option B is correct. A common mistake is to treat a - 4 itself as the slope before dividing the entire equation by 2.

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.

To identify slope and y-intercept, rewrite the equation in slope-intercept form y = mx + b. Starting with 7x − 8y + 24 = 0, move the other terms to obtain −8y = −7x − 24. Dividing every term by −8 gives y = (7/8)x + 3. Comparing with y = mx + b, the slope m is 7/8 and the y-intercept b is 3, so option A is correct. A common error is to read coefficients directly from the general form or to lose the sign while dividing by −8. The intercept is also confirmed by setting x = 0, which gives y = 3.

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.