Question 921821: Find the distance between these equations and give their x and y intercepts.
2x+3y=20
2x+3y=30 Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! 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:
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.
