Question

What is the point-slope form of the equation of a line that passes through the point (1, 4) and has a slope of −3?

Answer 1

Line through a point with known slope

\(\color{teal}{m} \)= 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)
\(\color{teal}{m} = \color{teal}{2.5}\)
\((\color{blue}{x_0},\color{purple}{y_0})=(\color{blue}{4},\color{purple}{3})\)
\(L: (y-\color{purple}{3}) = \color{teal}{2.5} (x-\color{blue}{4}) => y-\color{purple}{3}=\color{teal}{2.5}x-10 => y = 2.5x-7\)