Question

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

Answer 1

SOLUTION

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

$m_1\times m_2=-1$

From here, we have that

$\begin{gathered} m_1\times m_2=-1 \\ -2_{}\times m_2=-1 \\ m_2=\frac{-1}{-2} \\ m_2=\frac{1}{2} \end{gathered}$

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

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

Hence the answer is

$y=\frac{1}{2}_{}x+\frac{5}{2}$