Question

The line passing through the points (-7,4) and (-23,y) is parallel to a line that has a slope of -5/8. What is the value of y?

Answer 1

Two lines that are parallel to each other, will have the same slope.

so if this line is parallel to another with a slope of -5/8, the slope of this line is also -5/8 then.  We also know that it passes through -7, 4 and -23, y, let's do some checking.

$\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) &({{ -7}}\quad ,&{{ 4}})\quad % (c,d) &({{ -23}}\quad ,&{{ y}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{y-4}{-23-(-7)}\implies \cfrac{y-4}{-23+7} \\\\\\ \cfrac{y-4}{-16}=\boxed{-\cfrac{5}{8}}\implies 8y-32=80\implies 8y=112 \\\\\\ y=\cfrac{112}{8}\implies y=14$