Question

Which of the following equations is 2x + 3y = 6 written in slope-intercept form.

y=-(2/3)x + 6
y=-(2/3)x + 2
y=-(3/2)x + 2

Answer 1

y=(2/3)×+2 yuhhuhyhhy

Answer 2

The equation
`y=-(2)/(3)x+2`

Explanation:

Equations of the form
`ax+by=c` are known as Standard Form for a linear equation in two variables, x and y, in the case of your equation
`2x+3y=6` where a = 2, b = 3 and c = 6.

Equations of the form
`y = -(ax)/(b)+(c)/(b)` are known as Slope-Intercept form. This is called in this way because
`-(a)/(b)` is equal to the slope of the line, and
`(c)/(b)` is the value of y when x = 0, which makes it the y-intercept.

To convert from standard form
`2x+3y=6` to slope-intercept form
`y = -(ax)/(b)+(c)/(b)`, we need to follow these steps:

1. Subtract 2x from both sides
   `2x+3y-2x=6-2x`
2. Simplify
   `3y=6-2x`
3. Divide both sides by 3
   `(3y)/(3) =(6)/(3)-(2x)/(3)`
4. Simplify
   `y = 2-(2x)/(3) = -(2x)/(3) + 2`