Question

What is the equation in point-slope form of the line passing through (0, 5) and (−2, 11)?

y − 5 = −3(x + 2)

y − 5 = 3(x + 2)

y − 11 = −3(x − 2)

y − 11 = −3(x + 2)

Answer 1

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 0}}\quad ,&{\color{blue}{ 5}})\quad &({\color{red}{ -2}}\quad ,&{\color{blue}{ 11}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\

y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 2

y − 5 = −3(x + 2) ?

Answer 3

hmm if you pick the 5 from (0, 5)
then that'd be \(\bf y − 5 = −3(x -0)\)