Final answer:
To find the gradient and y-intercept of the line equation 3y - 2x = 6, we rearrange it into the form y = mx + b, resulting in y = (2/3)x + 2. The gradient is (2/3) and the y-intercept is 2.
Step-by-step explanation:
The equation of a straight line is given as 3y - 2x = 6. To find the gradient and the y-intercept, we need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m is the gradient, and b is the y-intercept.
Firstly, we rearrange the given equation to solve for y:
- Add 2x to both sides of the equation to get 3y = 2x + 6.
- Divide each term by 3 to isolate y, resulting in y = (2/3)x + 2.
From this form, we can see that the gradient (slope) of the line is (2/3) and the y-intercept is 2. The gradient represents the rise over the run, which means for every increase of 3 units on the horizontal axis (run), the vertical axis (rise) increases by 2 units. The y-intercept represents the point at which the line crosses the y-axis, which in this case is at the point (0, 2).