Question

Find an equation of the line perpendicular to y = - 2x + 6 that crosses the point(-2,8). Write your equation in slope-intercept form.

Answer 1

To solve this problem, the first step is to find the slope of the line. With the given information, we know that the line is perpendicular to y=-2x+6, find the slope of the line by knowing that the product of the slopes of two perpendicular lines is -1.

`\begin{gathered} m1\cdot m2=-1 \\ -2\cdot m2=-1 \\ m2=-(1)/(-2) \\ m2=(1)/(2) \end{gathered}`

With this slope and the given point, use the point slope formula to find the equation of the line in slope intercept form.

`\begin{gathered} y-y1=m(x-x1) \\ y-8=(1)/(2)(x-(-2)) \\ y-8=(1)/(2)(x+2) \\ y-8=(1)/(2)x+1 \\ y=(1)/(2)x+9 \end{gathered}`