Question

Please Explain/Show your work!

Answer 1

Check the picture below.

so, we have two points this line passes through, well, more than two points really, but let us use these two points to get its slope.

keeping in mind that the the constant of proportionality is simply the slope.

$\bf (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0.7}~,~\stackrel{y_2}{0.3}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{0.3-0}{0.7-0}\implies \cfrac{0.3}{0.7}\implies \cfrac{~~\frac{03}{10}~~}{\frac{07}{10}} \\\\\\ \cfrac{3}{10}\cdot \cfrac{10}{7}\implies \cfrac{10}{10}\cdot \cfrac{3}{7}\implies \blacktriangleright \cfrac{3}{7} \blacktriangleleft$