Write equations of parallel and perpendicular lines

Question

Write the equation of a line that is parallel to y=−32x−1y=−23​x−1y, equals, minus, start fraction, 3, divided by, 2, end fraction, x, minus, 1 and that passes through the point (4,6)(4,6)left parenthesis, 4, comma, 6, right parenthesis.

Answer 1

If your question is - Write the equation of a line that is parallel to y=−3/2x−1 and that passes through the point (4,6) then the solution is as follows:

y = -3/2x - 1 is in slope intercept form with slope m = -3/2

A line parallel to this line will have the same slope (-3/2)

Writing equation, in a point slope form, of line that passes through point (4,6) and has slope m = -3/2,

y-6 = -3/2(x-4)

y-6 = -3/2x + 6

y = -3/2x + 12. this is the equation of line that is parallel to y = -3/2x - 1 and passes through point (4,6).

let's check the answer, the equation y = -3/2x + 12 should pass through point (4,6) so placing 4 for x should give 6 as the answer for y.

-3/2(4) +12 = -6 + 12 = 6 which is correct!