Question

Write the equation in slope-intercept form (y = mx + b) for 5x - 2y = 12.

a) y = -5x + 6
b) y = 5x + 6
c) y = 5x - 6
d) y = 5x + 12

Answer 1

None of the provided options (a) y = -5x + 6, (b) y = 5x + 6, (c) y = 5x - 6, (d) y = 5x + 12 matches the correct slope-intercept form of the equation 5x - 2y = 12, which is y = (5/2)x - 6. It seems there may have been a typo in the options given.

Step-by-step explanation:

To rewrite the equation 5x - 2y = 12 in slope-intercept form (y = mx + b), we must solve for y in terms of x. The steps to do this are as follows:

1. Move the term with x to the opposite side by subtracting 5x from both sides of the equation: -2y = -5x + 12.
2. Divide every term by the coefficient of y, which is -2, to get y isolated: y = (5/2)x - 6.

Now the equation is in slope-intercept form where the slope (m) is 5/2, and the y-intercept (b) is -6. So, looking at the options provided by the student, none of the choices perfectly match our answer. However, if there's a typo in the options and they meant to write y = (5/2)x - 6 instead of their listed options, then that would be the correct slope-intercept form of the equation.