Question

[PLEASE ANSWER] Precalculus Question (has 2 parts)

Answer 1

Part I

$\bf \begin{array}{l|lllllll} x&2&\boxed{4}&6&8&\boxed{10}&12&14\\\\ y&1&\boxed{6}&11&16&\boxed{21}&26&31 \end{array}\implies \begin{array}{llll} (4,6)\\\\ (10,21) \end{array}\\\\ -------------------------------$

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ 4}}\quad ,&{{ 6}})\quad % (c,d) &({{ 10}}\quad ,&{{ 21}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{21-6}{10-4}$


part II

$\bf y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \begin{array}{llll} \textit{plug in the values for } \begin{cases} y_1=6\\ x_1=4\\ m=\boxed{?} \end{cases}\\ \end{array}\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form}$


now, the form above is the point-slope form, and that'd be the equation, you can leave it like so, or you can solve for "y", and put it in slope-intercept, same equation though.