Write the equation of the line with an x-intercept at (0,2) and perpendicular to 3x+4y=12.

First you normalize 3x+4y=12 into y = - 3/4 x + 3 (dividing by 4).

Then you observe that the slope of the line is - 3/4 (it's always the factor with the x). A perpendicular line has the reciprocal slope. Reciprocal means inverted and negated. So - 3/4 becomes + 4/3.

The equation will thus look like y = 4/3 x + b. To find b, we fill in the given x intercept (0,2), (we get 2 = 4/3 * 0 + b). With x=0, b must be 2.

So the equation is: y = 4/3 x + 2

The answer is y=4/3+2