Question

Quick algebra 1 question for some points!

Answer 1

3)

$\frac{y}{x} = \frac{4}{ - 3} = \frac{8}{ - 6} = \frac{12}{ - 9} \\ this \: relation \: holds \: so \: y \: varies \\ directly \: with \: x$

$\frac{ 4}{3} m = \frac{8}{ - 6} \\ m = \frac{ \frac{ - 8}{6} }{ \frac{3}{ - 4} } = \frac{8 \times 4}{6 \times 3} = \frac{32}{18} = 2 \\ multipling \: by \: 2$

2)

$\frac{y}{x} = \frac{ - 40}{ - 0.5} = \frac{8}{2.5} = \frac{5}{4} \\ \frac{y}{x} = 80 = 3.2 = 1.25 \\ this \: is \: untrue \: so \: y \: is \: not \\ varying \: directly \: with \: x$

$no \: constant \: of \: variation$

4)

$\frac{y}{x} = \frac{21}{3} = \frac{31.5}{4.5} = \frac{38.5}{5.5 \\ } \\ \frac{y}{x} = 7 = 7 = 7 \\ y \: varies \: directl y\: with \: x \\ consant \: of \: var = \frac{y}{x} = 7$

5)

$\frac{y}{x} = \frac{30}{6} = \frac{35}{7} = \frac{96}{8} \\ \frac{y}{x} = 5 = 5 = 12 \\ y \: does \: not \: vary \: directly \: with \: x$