# Find The Equation For The Line Through (2,6) And Perpendicular To Y=-5/4x+1?

These are the only choices to choose from A. 5/4x+7/2  B. -4/5x+38/5  C. 4/5x+17/2  D. -5/4x+17/2
thanked the writer.
Oddman commented
A perpendicular line will have slope of -1/(-5/4) = 4/5. The only choice with such a slope is (C), but that equation is not satisfied at the point (2, 6).
Oddman commented
(D) will be a *parallel* line through the given point.
You can solve this problem knowing a few equations and rules about perpendicular lines.

Y = mx + b (where m is the slope of the line, and b is the y intercept.)
If two lines are perpendicular, their slopes are negative reciprocals.

The slope of the line y = -5/4x + 1 is -5/4, according to the equation for a line.

And according to the perpendicular lines law, we know that the line perpendicular to to y = -5/4x + 1 has a slope which is the negative reciprocal of -5/4.

To find the negative reciprocal, just switch the denominator and numerator, and you'll have the reciprocal. Then just change polarity of the slope from negative to positive.

So the slope of the perpendicular line is 4/5.

Now we can write the equation for the perpendicular line as such:

Y = 4/5x + b

Since the line passes through the point (2,6), we can plug these values into our equation to find the value of b.

6 = 4/5 * 2 + b
6 = 1.6 + b
4.4 = b

Now we have all of the information to write the equation of the perpendicular line:

Y = 4/5x + 4.4
thanked the writer. 