Question

Write an equation in slope - intercept form for the line that passes through the given paint andis perpendicular to the given equation.6.(2,6), y = -1/4x + 3

Answer 1

`\begin{gathered} POINT\text{ (x,y)=(2,6)} \\ PERPENDICULAR\text{ TO y=-}(1)/(4)x+3 \\ The\text{ searched line must be perpendicular to the last line equation, } \\ slope\text{ m}\Rightarrow perpendicular\text{ slope }-(1)/(m) \\ I\text{n this case} \\ m=-(1)/(4)\text{ }\Rightarrow\text{ perpendicular slope is -}(1)/(-(1)/(4)) \\ or\text{ }(1)/((1)/(4))=((1)/(1))/((1)/(4))=(1\cdot4)/(1\cdot1)=4 \\ \text{hence, the line equation is in the form} \\ y=4x+b \end{gathered}`
`\begin{gathered} \text{Now, the only thing to compute is the y-intercept`