Question

Problem #1 -Find the equation of the line with the given slope and containing the given point.

Answer 1

For 1)

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -7}}\quad ,&{{ 0}})\quad % (c,d) \end{array} \\\quad \\\\ % slope = m slope = {{\boxed{ m}}}= \cfrac{rise}{run} \implies \implies -\cfrac{3}{5} \\ \quad \\\\ % point-slope intercept y-{{ y_1}}={{\boxed{ m}}}(x-{{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\ \qquad \uparrow\\ \textit{point-slope form}$

for 2)

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -3}}\quad ,&{{ 17}})\quad % (c,d) &({{ -7}}\quad ,&{{ 37}}) \end{array} \\\quad \\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}} \\ \quad \\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\qquad \textit{plug in the values and solve for "y"}\\ \qquad \uparrow\\ \textit{point-slope form}$

then change the y= part to f(x) =