analyzing the steepness of the graph of a linear function\nwhich function will have the steepest graph?\n$y…

Explanation:

Step1: Recall slope - steepness relation

The steepness of a line $y = mx$ is determined by the absolute value of the slope $m$.

Step2: Calculate absolute values of slopes

For $y=-2x$, $|m_1| = |-2|=2$; for $y =-\frac{1}{2}x$, $|m_2|=\left|-\frac{1}{2}\right|=\frac{1}{2}$; for $y=\frac{3}{2}x$, $|m_3|=\left|\frac{3}{2}\right| = \frac{3}{2}$; for $y=\frac{5}{2}x$, $|m_4|=\left|\frac{5}{2}\right|=\frac{5}{2}$.

Step3: Compare absolute - value of slopes

We compare $\frac{1}{2},\frac{3}{2},2,\frac{5}{2}$. Convert $2$ to $\frac{4}{2}$. Then $\frac{1}{2}<\frac{3}{2}<\frac{4}{2}<\frac{5}{2}$.

Answer:

$y=\frac{5}{2}x$