Question

Write an equation of the line. Write the answer in slope-intercept form. The line passes through (0,5) and is perpendicular to the line x + 4y = 2.?

Answer 1

`\begin{gathered} y=mx+b \\ m=\text{slope} \\ b=y-\text{intercept} \end{gathered}`

The product of the slopes of 2 lines that are perpendicular is equals to negative 1. Therefore,

`\begin{gathered} m_1m_2=-1 \\ \end{gathered}`

x + 4y = 2

4y = 2 - x

y = 1/2 - 1/4 x

`\begin{gathered} m_1(-(1)/(4))=-1 \\ (-m_1)/(4)=-1 \\ -m_1=-4 \\ m_1=4 \end{gathered}`

Therefore,

`\begin{gathered} 5=4(0)+b \\ b=5 \\ y=4x+5 \end{gathered}`