Let's break down the problem:

1. Function $f(x) = 3x + 1$: This is a linear function with a slope of 3 and a y-intercept of 1.

2. Graph of $g(x)$: From the description, the graph of $g(x)$ intersects the y-axis at -5 and the x-axis at 1.5 (or $\frac{3}{2}$).

Now, let's analyze what this implies:

• Translation of the y-intercept: The function $f(x)$ has a y-intercept of 1, while $g(x)$ has a y-intercept of -5. This suggests a vertical translation. The shift in the y-direction is from $1$ to $-5$, which is a shift downward by 6 units.

• Slope of $g(x)$: The slope remains the same because the description does not mention any change in the steepness of the graph. Thus, the slope of $g(x)$ is still 3.

Translation in terms of units:

The function $f(x) = 3x + 1$ is translated 6 units down to get the function $g(x)$.

Function $g(x)$:

Since the slope of the graph is unchanged, and the y-intercept has shifted to -5, the equation for $g(x)$ is $g(x) = 3x - 5$.

Final answers:

1. The graph $g(x)$ is the graph of $f(x)$ translated 6 units down.
2. $g(x) = 3x - 5$.

Would you like further details or have any questions?

Here are some related questions to expand on this:

1. How can we determine the slope of a line from its graph?
2. What is the general form of a linear function, and how can we modify it for translations?
3. How do vertical and horizontal translations affect the graph of a function?
4. What are the differences between vertical and horizontal translations in linear functions?
5. How do you solve for x-intercepts and y-intercepts algebraically?

Tip: When translating graphs, remember that vertical shifts affect only the y-intercept, while horizontal shifts affect the x-values.