What is the equation of the line perpendicular to y=1/2x+1 that contains the point (-2,1)

Question

What is the eq of the line perpendicular to y=1/2x+1 that contains (-2,1)

 

Answer 1

Step #1 get slope m. m=1/2 from the equations using point-slope form y-y1=m(x-x1)

Step #2 For the perpendicular line, you have to find the perpendicular slope. The reference slope is m = 1/2, and, for the perpendicular slope, I'll flip this slope and change the sign. Then the perpendicular slope is m = – 2/1 or just -2.

Step #3 Substitute m into y-y1=m(x-x1) using the point given (-2,1)

y-1 =-2(x- (-2) )=>

y-1 = -2 (x +2 ) =>

y= -2x -4 + 1=>

y=-2x + 3 is the equation of the line perpendicular to y=1/2x + 1

 

I would expect that my explanation is easy to follow and if you might need any future help please email me to set up a lesson even if it's for one hour a week to work on any difficulties that you may have. I wish you the best of luck in your studies.

 

Thanks,

Alla

Answer 2

Hello Nikki. There is a clause that states if a function has a slope of x, then the slope of the line perpendicular to it will be -(1/x). In other words, the slope of the perpendicular line will be its reciprocal with the opposite of sign.

 

In this equation the slope is 1/2. Therefore, the slope of the line perpendicular to this line is going to be -2.

 

This line is written in what is called slope intercept form. The general form for slope intercept form is: y = mx + b, where m is the slope and b is the y-intercept. Another way of writing a line is in point-slope form: y - y₁ = m(x - x₁), where x₁ and y₁ are the coordinates for the point given.

 

Using this knowledge, we look at the problem and see that our point given is (-2, 1). Using this point and the slope we calculated to be -2, we can conclude that the formula for the desired line will be: y - 1 = -2(x + 2).

 

Hope this helped and good luck!