Question

Write an equation of the line containing the points (-6,19) and (-15,28)

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -6}}\quad ,&{{ 19}})\quad % (c,d) &({{ -15}}\quad ,&{{ 28}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{28-19}{-15-(-6)}\implies \cfrac{28-19}{-15+6} \\\\\\ \cfrac{9}{-9}\implies -1 \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-19=-1(x-(-6))\\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-19=-(x+6)$

Answer 2

(-6,19) (-15,28)

28-19/-15-(-6)= 9/-9= -1

19=(-1)(-6) + b
19= 6 +b
b= 13
Therefore:
y= -x + 13
Hope I helped :)