Matching Linear Functions to Their Graphs

Analyze the information for each function.

1. ⓐ This function has a slope of 2 and a y-intercept of 3. It must pass through the point (0, 3) and slant upward from left to right. We can use two points to find the slope, or we can compare it with the other functions listed. Function $g$ has the same slope, but a different y-intercept. Lines I and III have the same slant because they have the same slope. Line III does not pass through $\left(0,\text{ 3}\right)$ so $f$ must be represented by Line I.
2. ⓑ This function also has a slope of 2, but a y-intercept of $-3.$ It must pass through the point $\left(0,-3\right)$ and slant upward from left to right. It must be represented by Line III.
3. ⓒ This function has a slope of –2 and a y-intercept of 3. This is the only function listed with a negative slope, so it must be represented by line IV because it slants downward from left to right.
4. ⓓ This function has a slope of $\frac{1}{2}$ and a y-intercept of 3. It must pass through the point (0, 3) and slant upward from left to right. Lines I and II pass through $\left(0,\text{ 3}\right),$ but the slope of $j$ is less than the slope of $f$ so the line for $j$ must be flatter. This function is represented by Line II.

Now we can re-label the lines as in Figure 10.

Figure 10