Answer:
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
Step-by-step 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.