Find a point on 2x+6y=12 such that the distance from the x-axis is twice the distance from the y-axis.

Question

Find a point on 2x+6y=12 such that the distance from the x-axis is twice the distance from the y-axis.

Answer 1

2x + 6y = 12

is the same as

x + 3y = 6, a line with slope =-1/3 and y intercept = 2, x intercept = 6

it helps to plot the line, and intercepts (0, 2) and (6, 0). Connect them with a straight line

distances to the axes are equal at the midpoint of that line segment, (3,1). go left and up the line segment to get a distance greater to the x axis than the y axis.

the point you want is (x, 2x) plug that into the equation to get x + 3(2x) = 6, 7x = 6, x = 6/7, y =12/7

the point (6/7, 12/7) is a distance 6/7 from the y axis and 12/7 from the x axis