Our direct variation formula is y=kx, where y and x represent values and k represents a number that is the same in the formula no matter what y or x you plug in, or a constant. Therefore, to find x, we divide k from both sides to get y/k=x using the inverse property of multiplication. To find k, we divide both sides by x to get y/x=k. Therefore, for 7, we have -4 (the y value)/10 (the x value)=k. Therefore, when x=5, we use y=kx to get 5(-4/10)=-2=y when x=5 For 8, we have 12/(-15)=4/(-5)=-4/5=k, so when x=2, we have y=2(-4/5)=-8/5 when x=2. Finally, for 9, we have 9/8=k, so since we have y/k=x, we have 18/(9/8)=x= [tex] \frac{ \frac{18}{1} }{\frac{9}{8} } = \frac{18}{1} * \frac{8}{9} =16[/tex]
Note that when we divide two fractions (and 18=18/1, similar to how 2=2/1), we can multiply the top fraction by the reciprocal of the bottom function, or the result when you switch the numerator (the top number) and denominator (the bottom number) of the fraction