Question

Please help! i will fan

Choose the equation below that represents the line that passes through the point (2, 4) and has a slope of 3.

y − 4 = 3(x − 2)
y − 2 = 3(x − 4)
y + 4 = 3(x + 2)
y + 2 = 3(x + 4)

Answer 1

Similar example: What is the equation of the line that has a slope of 9 and goes through the point (7,15) ?


Slope = \(\Large \color{red}{9}\)
The line goes through the point \(\Large (\color{green}{7},\color{blue}{15})\)


\[\Large \color{red}{m} = \color{red}{9}\]
\(\Large (\color{green}{x_1},\color{blue}{y_1})=(\color{green}{7},\color{blue}{15}) \rightarrow \color{green}{x_1}=\color{green}{7} \text{ and } \color{blue}{y_1}=\color{blue}{15}\)


Point Slope form

\[\Large y - y_1 = m(x - x_1)\]

\[\Large y - \color{blue}{y_1} = \color{red}{m}(x - \color{green}{x_1})\]

\[\Large y - \color{blue}{15} = \color{red}{9}(x - \color{green}{7})\]

Answer 2

Another example: What is the equation of the line that has a slope of -2 and goes through the point (-1,5) ?


Slope = \(\Large \color{red}{-2}\)
The line goes through the point \(\Large (\color{green}{-1},\color{blue}{5})\)


\[\Large \color{red}{m} = \color{red}{-2}\]
\(\Large (\color{green}{x_1},\color{blue}{y_1})=(\color{green}{-1},\color{blue}{5}) \rightarrow \color{green}{x_1}=\color{green}{-1} \text{ and } \color{blue}{y_1}=\color{blue}{5}\)


Point Slope form

\[\Large y - y_1 = m(x - x_1)\]

\[\Large y - \color{blue}{y_1} = \color{red}{m}(x - \color{green}{x_1})\]

\[\Large y - \color{blue}{5} = \color{red}{-2}(x - (\color{green}{-1}))\]

\[\Large y - 5 = -2(x + 1)\]