Question

Julia found the equation of the line perpendicular toy = -2x + 2 that passes through (5.-1).Analyze Julia's work. Is she correct? If not, what washer mistake?1 y25= 1/2 (-2) + 6Yes, she is correct,No, she did not use the opposite reciprocal for theslope of the perpendicular line.No, she did not substitute the correct x and yvaluesNo she did not apply inverse operations to solve forthe y-intercept.3+5b=555y=x5.5

Answer 1

The given line is

`y=-2x+2`

The line passes through (5, -1),

Perpendicular lines have opposite slopes, so we use the following equation to find the new slope knowing that the slope of the given line is -2.

`\begin{gathered} m\cdot m_1=-1 \\ m\cdot(-2)=-1 \\ m=(-1)/(-2) \\ m=(1)/(2) \end{gathered}`

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

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-1)=(1)/(2)(x-5) \\ y+1=(1)/(2)x-(5)/(2) \\ y=(1)/(2)x-(5)/(2)-1 \\ y=(1)/(2)x+(-5-2)/(2) \\ y=(1)/(2)x-(7)/(2) \end{gathered}`

Therefore, the equation of the new perpendicular line is

`y=(1)/(2)x-(7)/(2)`

So, she's not correct, she didn't substitute the correct x and y values.

The right answer is C.