Question

9. Write the slope-intercept form of the equation of theline through (3, 4) and perpendicular to y = -2x – 4.

Answer 1

From the line

`y=-2x-4`

Comparing this to equation of a line in the form of

`y=mx+c`

m= -2.

Let this be the first slope. Hence

`m_1=-2`

When two lines are perpendicular, their slope is related by the formula

`m_1* m_2=-1`

From here, we have that

`\begin{gathered} m_1* m_2=-1 \\ -2_{}* m_2=-1 \\ m_2=(-1)/(-2) \\ m_2=(1)/(2) \end{gathered}`

Equation of a line in lope-intercept form is give as

`\begin{gathered} y-y_1=m(x-x_1) \\ \end{gathered}`

Using m2 to represent m in the equation we have

`\begin{gathered} y-y_1=m(x-x_1) \\ y-y_1=m_2(x-x_1) \\ \end{gathered}`

Where y1 = 4 and x1 = 3, our equation becomes

`\begin{gathered} y-y_1=m_2(x-x_1) \\ y-4_{}=(1)/(2)_{}(x-3_{}) \\ y-4_{}=(1)/(2)_{}x-(3)/(2) \\ y=(1)/(2)_{}x-(3)/(2)+4 \\ y=(1)/(2)_{}x+(5)/(2) \end{gathered}`

Hence the answer is

`y=(1)/(2)_{}x+(5)/(2)`