Question

Convert the equation 3x -4y =12from standard form to slope-intercept form.

a. y=3/4 X-3
b. y=3/4 X+3
c. y= -3/4 X+3
d. y= -3/4 X-3

Answer 1

The equation 3x - 4y = 12 can be converted to slope-intercept form (y = mx + b) by isolating y on one side. The correct slope-intercept form is y = 3/4x - 3.

Step-by-step explanation:

Converting from Standard Form to Slope-Intercept Form

To convert the equation 3x - 4y = 12 from standard form to slope-intercept form, we must isolate y on one side of the equation. Here's a step-by-step process:

1. Begin with the standard form: 3x - 4y = 12
2. Subtract 3x from both sides to get: -4y = -3x + 12
3. Divide every term by -4 to isolate y: y = (3/4)x - 3

The resulting equation, y = 3/4x - 3, is in slope-intercept form, which can be written as y = mx + b, where m is the slope and b is the y-intercept.

Therefore, the correct answer is b. y = 3/4x + 3 (This is an error; please note that the correct conversion is y = 3/4x - 3).