Question

Which of these is a point-slope equation of the line that is perpendicular toy-25 = 2(x-10) and passes through (-3,7)?-O A. y+ 7 = 2(x-3)O B. y- 7 = -2(x+3)O C. y-7=-(x+3)O D.y+7=-1(x-3)-

Answer 1

We have to find the equation of the line, in point-slope form, that is perpendicular to y - 25 = 2(x - 10) and passes through (-3,7).

The line y - 25 = 2(x - 10) has a slope m = 2.

Perpendicular lines have slopes that are negative reciprocals, so our line will have a slope that is:

`m=-(1)/(m_p)=-(1)/(2)`

Then, we have the slope m = -1/2 and the point (-3,7), so we can write the point-slope form of the equation as:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-7=-(1)/(2)(x-(-3)) \\ y-7=-(1)/(2)(x+3) \end{gathered}`

Answer: y - 7 = -1/2 * (x + 3) [Option C]