Slope and y-intercept

Correct answer: A. slope = 2/3, y-intercept = 3

The governing idea is that in y = mx + c, m is the slope and c is the y-intercept. Rearrange the equation carefully: 2x − 3y + 9 = 0 gives −3y = −2x − 9. Dividing each term by −3 produces y = (2/3)x + 3. Consequently, the slope is 2/3 and the line crosses the y-axis at (0, 3), so option A is correct. The negative signs in option B would correspond to an incorrect division. Options C and D do not result from isolating y and therefore mix up coefficients from the general form. The y-intercept can independently be checked by setting x = 0.

Correct answer: A. 11

Both equations are already in slope-intercept form y = mx + c, so the coefficients of x are their slopes. Equal slopes give t + 1 = 8, which leads to t = 7. The second line has constant term 2t - 3, so its y-intercept is 2(7) - 3 = 14 - 3 = 11. Therefore option A is correct. The number -4 is the intercept of the first line, not the second; 8 is the slope of the second line, not its intercept. The other choices do not result from the required substitution. Substituting t = 7 into the second equation produces y = 8x + 11, making the answer transparent and confirming that the y-intercept is the value of y when x = 0.

Correct answer: A. y-intercept 6, slope -6/7

The governing concept is y = mx + c, in which m is the slope and c is the y-intercept. Rearrange 6x + 7y - 42 = 0 by moving 6x and -42 to the other side: 7y = -6x + 42. Divide every term by 7 to obtain y = (-6/7)x + 6. Thus the slope is -6/7 and the y-intercept is 6, so option A is correct. Option B reverses both signs. Option C reads the original constant and coefficient as the answers without isolating y, and option D similarly mistakes the coefficient of y for the slope. Setting x = 0 in the original equation gives 7y - 42 = 0, hence y = 6, which confirms the intercept directly.

Correct answer: A. Slope 3/4, y-intercept 3

Use the slope-intercept form y = mx + c. Starting with 3x - 4y + 12 = 0, move 3x and 12 to the right side: -4y = -3x - 12. Divide the entire equation by -4, changing both negative signs: y = (3/4)x + 3. Therefore, the slope is m = 3/4 and the y-intercept is c = 3, so option A is correct. Option B fails because it retains incorrect signs after division. Option C confuses the coefficient of y with the slope, and option D copies values from the unrearranged equation rather than converting it to slope-intercept form. A direct check with x = 0 gives y = 3, confirming the intercept.