Question

match each equation to its graph.
a. (y = 2x)
b. (y=\frac{4}{5}x)
c. (y=\frac{1}{4}x)
d. (y=\frac{2}{3}x)
e. (y=\frac{4}{3}x)
f. (y=\frac{3}{2}x)

Explanation:

Step1: Recall slope - intercept form

The equations are in the form $y = mx$ where $m$ is the slope. A larger positive value of $m$ makes the line steeper.

Step2: Analyze slopes

For $y = 2x$, slope $m = 2$; for $y=\frac{4}{5}x$, slope $m=\frac{4}{5}=0.8$; for $y=\frac{1}{4}x$, slope $m = \frac{1}{4}=0.25$; for $y=\frac{2}{3}x$, slope $m=\frac{2}{3}\approx0.67$; for $y=\frac{4}{3}x$, slope $m=\frac{4}{3}\approx1.33$; for $y=\frac{3}{2}x$, slope $m = \frac{3}{2}=1.5$.

Step3: Match based on steepness

The steeper the line, the larger the absolute - value of the slope.

• The line with the smallest slope among the given is $y=\frac{1}{4}x$ (least steep).
• The line with the largest slope is $y = 2x$ (most steep).

Answer:

Match them by comparing slopes. For example, the least - steep line (with slope $\frac{1}{4}$) corresponds to the graph with the shallowest angle with the x - axis, and the most - steep line (with slope 2) corresponds to the graph with the steepest angle with the x - axis among the given graphs. Without specific labels on the graphs, we can't give a one - to - one labeled match, but the general method is to order the lines from least steep (smallest positive slope) to most steep (largest positive slope).