Question

what is the equation when dealing with the question, "What is the equation of a line that goes through a point"

Answer 1

`\begin{gathered} \text{ The equation that goes through a point }(x_1,y_1)\text{ is} \\ y-y_1=m(x-x_1)_{} \end{gathered}`
`\begin{gathered} \text{if we have a line }y=mx+b \\ \text{then the slope of the perpendicular line to the first satisfy nm=-1} \\ \\ \text{the initial line is y=-2x+5} \\ n(-2)=-1 \\ n=(-1)/(-2) \\ n=(1)/(2) \\ \text{Thus the new line is of the form} \\ \\ y=(1)/(2)x+b \\ \\ \text{ if it passes through the point (-4,1) then} \\ 1=(1)/(2)(-4)+b \\ 1=-2+b \\ 3=b \end{gathered}`
`y=(1)/(2)x+3`