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

Sagot :

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.

View image NationB753114
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