3x - 2y = 6
Your hint gives you a longer method of find the slope for the line. When we are given the equation of the line, we shouldn't bother to find two points. It's only when we are given a graph that using two points to find the slope is helpful.
To find the slope of 3x - 2y = 6, we first need to convert it into slope-intercept form.
Slope-intercept form is y = mx + b. Where m is the slope and b is the y-intercept.
If we solve for y in the equation they gave you, we have converted it into slope-intercept form and it will be easy to find the slope.
3x - 2y = 6
Add 2y on both sides.
3x = 6 + 2y
Subtract 6 on both sides.
3x - 6 = 2y
2y = 3x - 6
Divide by 2 on both sides.
y = (3/2)x - 3
This is now in the form of y = mx + b
y = (3/2)x - 3
y = mx + b
You can see that m = 3/2 and that b = -3
That means that the slope is 3/2 and that the y-intercept is -3.
The slope of the line 3x - 2y = 6 is 3/2 OR 1.5 OR 1 1/2.