find the equation of the line that is perpendicular to 5x−4y=−1 and passes through Point A(−3,2).

Answer 1

I would put 5x - 4y = -1 into slope-intercept form (y = mx + b) so that way you find the slope easily. A line that is perpendicular to another line has a negative reciprocal slope to that line (ie 2/3 --> -3/2).

So let's solve for y in 5x - 4y = -1 --> -4y = -5x - 1 --> y = 5/4x + 1/4.

Because the slope in the above equation is 5/4, now find its negative reciprocal to find the other line that is perpendicular to this line. 5/4 --> -4/5.

The new slope (= m) for the other line is -4/5.

Now let's use the point (-3, 2) and slope of -4/5 and plug into y = mx + b.

2 = (-4/5)*-3 + b. Solve for b: 2 = 12/5 + b --> b = -2/5.

So the equation is y = -4/5x - 2/5

I hope this helps!