Let's break this problem down step-by-step.

We are given two functions:

1. The function in the graph appears to be $f(x)$, and we are tasked with identifying its slope and y-intercept.
2. The second function provided in the equation form is $g(x) = -2x + 3$.

Comparing the slopes:

1. For the graph function $f(x)$:

   • By observing the graph, the line has a negative slope. To calculate the slope, we look at two points on the graph: one at $(0, 3)$ (the y-intercept) and another at $(-5, 5)$.
   • Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{5 - 3}{-5 - 0} = \frac{2}{-5} = -\frac{2}{5}$.
   • So, the slope of $f(x)$ is $-\frac{2}{5}$.

2. For the function $g(x) = -2x + 3$:

   • The slope is clearly $-2$ because the equation is in slope-intercept form, $y = mx + b$, where $m$ is the slope.

Comparing the y-intercepts:

1. For $f(x)$:

   • From the graph, the y-intercept occurs at $(0, 3)$, meaning the y-intercept is 3.

2. For $g(x) = -2x + 3$:

   • The y-intercept is also 3 because the equation $g(x) = -2x + 3$ shows that when $x = 0$, $g(0) = 3$.

Conclusion:

• The slopes are different: $-\frac{2}{5}$ for $f(x)$ and $-2$ for $g(x)$.
• The y-intercepts are the same: 3 for both functions.

Therefore, the correct answer is D. The slopes are different but the y-intercepts are the same.

Would you like more details on the slope calculation or how to interpret the graph?

Here are 5 follow-up questions that you might find helpful:

1. What does the slope of a line tell us about the graph?
2. How do you find the slope of a line from two points on the graph?
3. What is the significance of the y-intercept in a linear equation?
4. How would the graph of $g(x) = -2x + 3$ look compared to $f(x)$?
5. Can you explain the difference between positive and negative slopes?

Tip: Always remember that the slope of a line measures its steepness, and a negative slope indicates a line that falls as you move from left to right!