Question 921821
to find the y intercept, set x = 0 and solve for y.
2x + 3y = 20 becomes 3y = 20 which becomes y = 20/3 = 6 and 2/3
2x + 3y = 30 becomes 3y = 30 which becomes y = 30/3 = 10


to find the x intercept, set y = 0 and solve for x.
2x + 3y = 20 becomes 2x = 20 which becomes x = 10
2x + 3y = 30 becomes 2x = 30 which becomes x = 15


the vertical distance between these equations is going to be 30/3 - 20/3 = 10/3 = 3 and 1/3.


to find the slope, solve each equation for y.
2x + 3y = 20 becomes y = -2/3*x + 20/3
2x + 3y = 30 becomes y = -2/3*x + 30/3


the slopes are the same so the graphs of the equations are parallel to each other.


the graphs of the equations looks like this:


{{{graph(600,600,-20,20,-20,20,-2/3*x + 20/3, -2/3*x + 30/3)}}}


you can see that the y intercepts are 30/3 and 20/3 which are equivalent to 10 and 6 and 2/3.


you can see that the x-intercepts are equal to 10 and 15.


the slope of -2/3 means that the y value goes down 2 units for every 3 units that the x value goes to the right.