Question

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

Answer 1

Answer: y = -x

Explanation:

Perpendicular lines have opposite reciprocal slopes.

Let's first find the slope of
`y=x+3` - the slope is 1.

Now, the opposite reciprocal of 1 is ... -1 ,so the new line has a slope of -1.

Let's use our point-slope formula to find the equation of the line . Remember, Point - slope is :

`\LARGE\boldsymbol{\sf{y-y_1=m(x-x_1)}}`

where —

• m -> slope
• (x₁, y₁) is a point on the line

From the given data, we deduce that -

• m = -1
• point = (2,-2)

Now, we plug the data into the formula:

`\large\begin{gathered}\boldsymbol{\sf{y-(-2)=-1(x-2)}}\\\boldsymbol{\sf{y+2=-(x-2)}}\\\boldsymbol{\sf{y+2=-x+2}}\\\boldsymbol{\sf{y=-x+2-2}}\\\boldsymbol{\sf{y=-x}}\end{gathered}}}`

The new line's equation is y = -x.