how do you represent the x-interept of the graph y=2/3x+6?

Answer 1

for the x-inercept let y = 0
0 = (2/3)x + 6
0 = 2x + 18
x = -9

if you want to re-arrange the equation so that the x-intercept can be read, like the b in y=mx + b is the y-intercept, solve the equation for x

y = (2/3)x + 6
3y = 2x + 18
2x = 3y - 18
x = (3/2)y - 9

notice that the constant at the end is the x-intercept, just like the b in y = mx +b was the y-intercept,
BUT, notice that the number in front of y is NOT the slope, instead it is the reciprocal of the slope.