Write an equation of the line that passes through the point P and is perpendicular to the line with the given equation: P(5,3); y = 5x + 2

Question

Write an equation of the line that passes through the point P

and is perpendicular to the line with the given equation:

P(5,3); y = 5x + 2

Answer 1

Hello,

So the thing we have to remember about perpendicular lines is that their slopes are opposite-signed reciprocals of each other. Positives become negative and negatives, positive. Numerators and denominators are switched.

In standard form, y=mx+b, the reciprocal of the standard line would read y=-(1/m)x+b.

Therefore, since the slope m of the given line is positive five, the slope of the perpendicular line is -1/5 [since 5 can also be expressed as 5/1].

Our first part is complete. Now, since the new line crosses the given point at (5,3), we can use the x-and y-coordinates of that point to get the y-intercept of our line, since we only have the slope thus far. Input them into their respective places from the coordinates to the standard form.

Start with standard form.

y=mx+b

Substitute known values for m, x, and y.

3 = -1/5(5) + b

Let's solve for b.

3 = -1 + b

3+1 = b

4 = b

Our answer is y=-1/5x+4

Answer 2

We can do this 2 ways. First, we need to realize that perpendicular lines have opposite, reciprocal slopes, so the slope of our new line will be -1/5.

Way # 1:

y - 3 = (-1/5)(x - 5)

y - 3 = (-1/5)x + 1

y = (-1/5)x + 4

Way# 2:

3 = (-1/5)(5) + b

3 = -1 + b

4 = b

y = (-1/5)x + 4