Question

Write the equation of the line in standard form that passes through point P(-5,7) andPerpendicular to the equation of the line y=-x+2.

Answer 1

The given equation is

`y=-x+2`

We have to find a new line perpendicular to the given line and must pass through P(-5,7).

First, we use the definition of perpendicularity for two lines.

`m_1\cdot m_2=-1`

Where one of the slopes is equal to -1 because the coefficient of x in the given equation is -1. Let's find the other slope.

`\begin{gathered} m\cdot(-1)=-1 \\ m=1 \end{gathered}`

This means the new perpendicular line has a slope of 1.

Now, we use the slope we found, the point P, and the point-slope formula, to find the equation.

`\begin{gathered} y-y_1=m(x-x_1) \\ y-7=1(x-(-5)) \\ y-7=x+5 \\ y=x+5+7 \\ y=x+12 \end{gathered}`

Therefore, the equation of the new perpendicular line is y = x + 12.