Question

A point is moving on a linear path. The coordinates of the starting point are (1, 5) and the ending point is (2, 10), what is the equation of the path?

Answer 1

Find the slope of the line connecting those two points with \[m = \frac{y_2-y_1}{x_2-x_1}\]then use the point-slope formula
\[y-y_1 = m(x-x_1)\]to write an equation for the line through those two points.

The problem is somewhat sloppily written, as it implies there is only one ("the") equation for the path, when in fact there are infinitely many equations describing the path.

Answer 2

ditto \(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 1}}\quad ,&{\color{blue}{ 5}})\quad &({\color{red}{ 2}}\quad ,&{\color{blue}{ 10}})
\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 3

Thanks! y – 5 = 5(x – 1)

y – 1 = 5(x – 5)

y – 5 = 4(x – 1)

y – 5 = 3(x – 1) These are my answer choices! But i dont see where the y comes from?? Help

Answer 4

hmmm what did you get for the slope?

Answer 5

\[\frac{ 10-5 }{ 2-1? } Then \frac{ ?5 }{ 1? } \]