Question

Write an equation of a line that is perpendicular to

the line y = 2/3x+5 and that passes through the
point (0,4).

Answer 1

y = (-3/2)x + 4

Explanation:

The slope of the given line is 2/3. The slope of any line perpendicular to the given line is the negative reciprocal of 2/3, which comes out to -3/2.

Now we have the slope of the new line and know that it passes through (0, 4). (0, 4) happens to be the y-intercept, b, in y = mx + b:

Substituting -3/2 for m and 4 for b, we get y = (-3/2)x + 4.