Question

Get the equation into slope-intercept form (y = mx + b)

Equation: 2x - 3y = 6

Answer 1

`y = (2)/(3)x - 2`

Explanation:

Pre-Solving

We are given the equation 2x - 3y = 6, which we want to get into slope-intercept form.

As the question has told us, slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

The equation is currently written in standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot be 0. a is usually non-negative as well.

Solving

We will need to turn standard form into slope-intercept form.

To do this, we need to solve the equation for y, which means that we put the value of y on one side, and everything else on the other.

2x - 3y = 6

Start by subtracting 2x from both sides

2x - 3y = 6

-2x -2x
______________

-3y = -2x + 6

Now, divide by -3.

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

We can simplify this.

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

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

`y = (2)/(3)x - 2`

Answer 2

`y=(2)/(3)x-2`

Explanation:

Given equation:

`2x-3y=6`

Add 3y to both sides:

`\implies 2x-3y+3y=6+3y`

`\implies 2x=6+3y`

Subtract 6 from both sides:

`\implies 2x-6=6+3y-6`

`\implies 2x-6=3y`

`\implies 3y=2x-6`

Divide both sides by 3:

`\implies (3y)/(3)=(2x)/(3)-(6)/(3)`

`\implies y=(2)/(3)x-2`

Slope-intercept form:

`\boxed{y=mx+b}`

Where:

• m = slope
• b = y-intercept

Compare the rearranged given equation with the slope-intercept form:

• Slope = ²/₃
• y-intercept = -2