Question

Find the equation of the line passes through (2,5) and perpendicular to 2x + 3y=5

Answer 1

Answer:

y - 5 = (3/2)(x - 2)

Step-by-step explanation:

If two lines are perpendicular, their slopes are negative reciprocals of one another.

The slope of 2x + 3y = 5 is found by solving this equation for y:

3y = -2x + 5, or y = (-2/3)x + 5/3.

Thus, the slope of the new line is the negative reciprocal of -2/3, which in turn comes out to 3/2.

Use the point-slope formula y - k = m(x - h):

Substituting the givens, we get  y - 5 = (3/2)(x - 2)