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

what is point slope form first?

Answer 2

y - y_1 = m(x - x_1). plug and chug theh slope and points into the equatoin: http://www.purplemath.com/modules/strtlneq2.htm

Answer 3

Point-slope form of equation of a line

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

Answer 4

Given slope m=-3
(x0,y0)=(1,4)
slope equation
y-y0=m(x-x0)
y-4=-3(x-1)
y-4=-3x+3
y=-3x+7

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