Question

The equation of a line is: y = 4/7x - 12Which equation would have a line that is perpendicular to this line?1. y = - 4/7x - 12. y = - 7/4x - 53. y = 7/4x - 84. y = 4/7x - 2

Answer 1

Explanation

Let's recall the framework of the equation of a line:

We say that two lines are perpendicular if the slope of one line is minus the multiplicative inverse of the slope of the other one; mathematically, this amounts to the following equation:

$m_1=-\frac{1}{m_2}.\leftarrow\begin{cases}m_1=\text{Slope of one line} \\ m_2=\text{ Slope of the other line}\end{cases}$

In this case, the slope of our line is 4/7. Then the slope (m) of any line perpendicular to it must satisfy

$m=-\frac{1}{\frac{4}{7}}\text{.}$

Solving this equation for m, we get

$\begin{gathered} m=-\frac{1}{\frac{4}{7}}, \\ m=-\frac{\frac{1}{1}}{\frac{4}{7}}, \\ m=-\frac{1}{1}\cdot\frac{7}{4},\leftarrow\text{ Flipping rule when dividing fractions} \\ m=-\frac{7}{4}. \end{gathered}$Answer

The answer is 2.