Question

problem 3
match each equation to its graph
graph 1
graph 2
graph 3
graph 4
graph 5
graph 6
a. y = 2x
b. y=\frac{1}{2}x
c. y=\frac{1}{4}x
d. y=\frac{3}{2}x
e. y=\frac{1}{3}x
f. y=\frac{1}{5}x

1. graph 1
2. graph 2
3. graph 3
4. graph 4
5. graph 5
6. graph 6

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope. For equations of the form $y=mx$ (where $b = 0$), the slope determines the steepness of the line.

Step2: Analyze slopes

For $y = 2x$, the slope $m = 2$. A slope of 2 means for every 1 - unit increase in $x$, $y$ increases by 2 units. This is a relatively steep line.
For $y=\frac{1}{2}x$, the slope $m=\frac{1}{2}$. For every 2 - unit increase in $x$, $y$ increases by 1 unit.
For $y=\frac{1}{4}x$, the slope $m=\frac{1}{4}$. It has a gentle slope.
For $y=\frac{3}{2}x$, the slope $m=\frac{3}{2}$. For every 2 - unit increase in $x$, $y$ increases by 3 units.
For $y=\frac{1}{3}x$, the slope $m=\frac{1}{3}$.
For $y=\frac{1}{5}x$, the slope $m=\frac{1}{5}$.

Step3: Match equations to graphs

• $y = 2x$ (A) has a steep positive - slope and matches Graph 5.
• $y=\frac{1}{2}x$ (B) has a moderate positive - slope and matches Graph 2.
• $y=\frac{1}{4}x$ (C) has a gentle positive - slope and matches Graph 4.
• $y=\frac{3}{2}x$ (D) has a relatively steep positive - slope and matches Graph 6.
• $y=\frac{1}{3}x$ (E) has a moderate positive - slope and matches Graph 1.
• $y=\frac{1}{5}x$ (F) has a very gentle positive - slope and matches Graph 3.

Answer:

A. Graph 5
B. Graph 2
C. Graph 4
D. Graph 6
E. Graph 1
F. Graph 3