Question

What is the equation in point-slope form of the line passing through (−2, 0) and (2, 8)?

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

Answer 1

Point-slope form: \(\large y - y_1 = m(x - x_1)\)

Find the slope: \(\large \frac{y_2 - y_1}{x_2 - x_1}\)

Have \(y_1 = -2 \) and \(x_1 = 0\). The \(y\) and \(x\) in the formula will just stay as it is.

Answer 2

\(\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
% (a,b)
&({\color{red}{ -2}}\quad ,&{\color{blue}{ 0}})\quad
% (c,d)
&({\color{red}{ 2}}\quad ,&{\color{blue}{ 8}})
\end{array}
\\\quad \\
% slope = m
slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies
\cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}
\\ \quad \\
% point-slope intercept
y-{\color{blue}{ y_1}}={\color{green}{ m}}(x-{\color{red}{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\
\qquad \uparrow\\
\textit{point-slope form}\)

Answer 3

\[x _{1}=-2,y _{1}=0,x _{2}=2,y _{2}=8\]
eq. of a line through two points is
\[y-y_{1}=\frac{ y _{2}-y _{1} }{ x _{2}-x _{1} }\left( x-x _{1} \right)\]

Answer 4

you can take any point as (x1,y1) and other as (x2,y2)