Let's find the slope of this line using the principle of rise over run. The difference of the y-coordinates divided by the difference of the x-coordinates will yield the slope of the line. If we call the slope m, we have:
m = (0 - (-5))/(6 - 3) = (0 + 5)/(3) = 5/3
Now, let's use the slope-intercept form of the equation of a line, where b = the y-intercept. We can use either of the two given points as our values for x and y. Let's choose the second one.
y = mx + b
0 = (5/3)(6) + b
0 = (30/3) + b
0 = 10 + b
-10 = b
The equation of the line is y = (5/3)x - 10 in slope-intercept form.
Standard form is Ax + By = C
We can multiply both sides of the above equation of the line by 3.
3y = 5x - 30
3y + 30 = 5x
5x - 3y = 30
