Question

Write the slope-intercept form of the equation of each line.

Through: (2,-2), perpendicular to y=-2x+3

Answer 1

Greetings!

Answer:

2y = x - 6

Explanation:

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

This is the number in front of the x.

Seeing as this is -2x, the slope of this line is -2

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

So, in this case it is:

`(-1)/(-2)`

The negatives cancel out which leave
`(1)/(2)`

So the gradient is
`(1)/(2)`

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

y - y1 = m(x - x1)

Where ya and x1 are the values in the coordinates (2 , -2)

So y1 = -2, x1 = 2, and m is a half. Plug these values in:

y - - 2 =
`(1)/(2)(x - 2)`

We need to get rid of the half so we multiply the whole equation by 2:

2y - - 4 = (x - 2)

The minus and the negative turn into a positive:

2y + 4 = x - 2

And now simply move the +4 over to the other side, making it a negative:

2y = -2 - 4 + x

Simplify:

2y = x - 6

So the equation of the line is 2y = x - 6

Hope this helps!