What is the gradient of the line 3y=2x-6

2/3

Step-by-step explanation:

The gradient of any line in standard form, Ax + By = C is - A/B.

Divide each term by 3 and simplify.

3y = 2x - 6

3y / 3 = y

2x / 3 = 2/3x

6 / 3 = 2

So, y = 2 / 3 x - 2

slope or gradient = 2/3

Explanation:

The first step in finding the slope of a line that is written in standard form is to write the equation in slope-intercept form, y=mx+b. To do this, rearrange the variables. The standard form, Ax + By = C can be rewritten as By = - Ax + C.

Divide by B to simplify

In the equation By = - Ax + C, B needs to be distributed through the equation. To do this, divide both sides by B. The answer is y = (-A/B) x + C/B.

Find the slope

Once the equation of the line is in slope-intercept form and is simplified, then the slope equals the term in front of the x variable. In the standard form from step 2, the slope is - A/B.