For the following problem, indicate the line where the mistake is (if any) and explain how it can be corrected. Be sure to include the correct answer. Determine the slope of the following linear equation: 6x + 4y = -7. The provided work is: (1) 6x + 4y = -7; (2) 4y = -6x - 7; (3) y = (-6x - 7) / 4; (4) y = -6/4x - 7/4; (5) y = -3/2x - 7/4; (6) m = -7/4.

For the following problem, indicate the line where the mistake is (if any) and explain how it can be corrected. Be sure to include the correct answer. Determine the slope of the following linear equation: 6x + 4y = -7. The provided work is: (1) 6x + 4y = -7; (2) 4y = -6x - 7; (3) y = (-6x - 7) / 4; (4) y = -6/4x - 7/4; (5) y = -3/2x - 7/4; (6) m = -7/4.

Answer

The mistake is in line (6). In the previous line (5), the equation was correctly simplified to the slope-intercept form, y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Line (5) shows y = -3/2x - 7/4. In this form, the coefficient of x represents the slope (m), and the constant term represents the y-intercept (b). Therefore, the slope 'm' should be -3/2. Line (6) incorrectly identifies -7/4 (the y-intercept) as the slope. To correct it, line (6) should state: m = -3/2.