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:
[tex]m_1=-\frac{1}{m_2}[/tex]Then, knowing the slope of the perpendicular line, m=-1/4, we can find the slope of our line as:
[tex]m=-\frac{1}{(-\frac{1}{4})}=\frac{1}{\frac{1}{4}}=4[/tex]Knowing the slope of our line, m=4, and one point, we can write the equation in slope-point form and rearrange as:
[tex]\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}[/tex]We can check the solution with a graph:
Answer: the equation of the line is y = 4x + 11.
