Question

Find the equation of a line that goes through the point ( - 3, - 1 ) and is perpendicular to the line: y = - 1 / 4x - 1.

Answer 1

We have to find the equation of a line that goes through point (-3,-1) and is perpendicular to the line y = -1/4*x-1.

We can find the slope of our line knowing that perpendicular lines have slopes that are negative reciprocals:

`m_1=-(1)/(m_2)`

Then, knowing the slope of the perpendicular line, m=-1/4, we can find the slope of our line as:

`m=-(1)/((-(1)/(4)))=(1)/((1)/(4))=4`

Knowing the slope of our line, m=4, and one point, we can write the equation in slope-point form and rearrange as:

`\begin{gathered} y-y_0=m(x-x_0) \\ y-(-1)=4(x-(-3)) \\ y=4(x+3)-1 \\ y=4x+12-1 \\ y=4x+11 \end{gathered}`

We can check the solution with a graph:

Answer: the equation of the line is y = 4x + 11.