Question

what is the equation of the line that passes trough point (0,1) and (5,-2) MEDAL!!!!

Answer 1

I suggest the following:

Step 1: find the slope (m) between two points \(R(x_1,y_1)\) and \(S(x_2,y_2)\)
\(\Large m=\frac{y_2-y_1}{x_2-x_1}\)


Step 2: using the slope m found above, find the point-slope form of equation of the line

\(\color{teal}{m} \)= slope
\((\color{blue}{x_0},\color{purple}{y_0})\) = given point

Equation of line \(\boxed{\color{red}{L: y-\color{purple}{y_0} = \color{teal}{m} (x-\color{blue}{x_0})}}\)

Example:
Find equation of the line with slope 2.5 passing through the point (4,3)
\(\color{teal}{m} = \color{teal}{2.5}\)
\((\color{blue}{x_0},\color{purple}{y_0})=(\color{blue}{4},\color{purple}{3})\)
\(L: (y-\color{purple}{3}) = \color{teal}{2.5} (x-\color{blue}{4}) => y-\color{purple}{3}=\color{teal}{2.5}x-10 => y = 2.5x-7\)