Question

Write the slope-intercept form of the equation of the line described. 9.) through: ( 3 , 3 ) , perpendicular to Y= -3/4x

Answer 1

First, the slopes of two perpendicular lines satisfy

`\begin{gathered} m_1=(-1)/(m_2) \\ \text{ Where } \\ m_1=\text{ slope of line 1} \\ m_2=\text{ slope of line }2 \end{gathered}`

Then, if you take Y=-3/4x as line 1, you have

`\begin{gathered} m_1=(-3)/(4) \\ \text{ Using the formula above} \\ (-3)/(4)=(-1)/(m_2) \\ \text{Multiply both sides of equation by m2} \\ m_2\cdot(-3)/(4)=(-1)/(m_2)\cdot m_2 \\ _{}m_2\cdot(-3)/(4)=-1 \\ \text{ Multiply both sides of equation by }-(4)/(3) \\ m_2\cdot(-3)/(4)\cdot(-4)/(3)=-1\cdot(-4)/(3) \\ m_2\cdot(12)/(12)=(4)/(3) \\ m_2=(4)/(3) \end{gathered}`

Now, using the point slope formula you have

`\begin{gathered} y-y_2=m_2(x-x_2) \\ y-3=(4)/(3)(x-3) \\ y-3=(4)/(3)x-(12)/(3) \\ y-3=(4)/(3)x-4 \\ \text{ Add 3 to both sides of the eqution} \\ y-3+3=(4)/(3)x-4+3 \\ y=(4)/(3)x-1 \end{gathered}`

Therefore, the slope-intercept form of the equation of the line described is

`y=(4)/(3)x-1`