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

Step-by-step 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=-(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=-(1)/((4)/(7))\text{.}`

Solving this equation for m, we get

`\begin{gathered} m=-(1)/((4)/(7)), \\ m=-((1)/(1))/((4)/(7)), \\ m=-(1)/(1)\cdot(7)/(4),\leftarrow\text{ Flipping rule when dividing fractions} \\ m=-(7)/(4). \end{gathered}`Answer

The answer is 2.