Question

Write an equation of the line perpendicular to the given line that contains P.

​P(4, -3); y=1/2x+3. Write an equation for the line in​ point-slope form.

Answer 1

Greetings!

Answer:

y = 2x - 5

Explanation:

First, we must find the slope of the current equation.

This is the number in front of the x.

Seeing as this is 1/2x, the slope of this line is 1/2

When finding the slope of a line perpendicular, you need to find the
`(-1)/(slope)`

So, in this case it is:

`(-1)/((1)/(2) )`

This gives the result -2, so the gradient on the perpendicular line is -2

Now, to find the equation of a line, you need to use:

y - y1 = m(x - x1)

Where y1 and x1 are the values in the coordinates (4 , -3)

So y1 = -3, x1 = 4, and m is a half. Plug these values in:

y - 3 =2(x - 4)

Expand the brackets by multiplying the contents by two:

x * 2 = 2x

-4 * 2 = -8

2x - 8

y - 3 = 2x -8

And now simply move the -3 over to the other side, making it a positive:

y = 2x - 8 + 3

Simplify:

y = 2x - 5

So the equation of the line is y = 2x - 5

Hope this helps!