Question

Use the image to answer the question.
<img alt="An illustration shows a coordinate plane with four quadrants. The x-axis and y-axis both range from negative 6 to 6 in one unit increments. A downward slanting line is graphed on the coordinate plane. The line passes through points plotted at left parenthesis 0 comma 3 right parenthesis, and left parenthesis 5 comma 1 right parenthesis. " height="800" src="

Determine if the given graph is the graph of the function y=−25x+3
𝑦
=
−
2
5
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+
3
. Enter 1 for yes. Enter 2 for no.

(1 point)

Answer 1

To determine if the graph given corresponds to the function \( y = -\frac{2}{5}x + 3 \), we can analyze the characteristics of both the graph and the equation.

1. **Slope Calculation**: The slope of the line described by the equation \( y = -\frac{2}{5}x + 3 \) is \( -\frac{2}{5} \), which means for every 5 units you move to the right (increasing \( x \)), the value of \( y \) will decrease by 2 units.

2. **Y-intercept**: The y-intercept of this function is at \( y = 3 \), which means the line crosses the y-axis at the point (0, 3).

3. **Comparison with Points on the Graph**: The graph passes through the points (0, 3) and (5, 1):
- The point (0, 3) matches the y-intercept.
- To confirm if the slope is correct, we can check the change in y when moving from (0, 3) to (5, 1):
- Change in y: \( 1 - 3 = -2 \)
- Change in x: \( 5 - 0 = 5 \)
- The slope (change in y / change in x) is \( \frac{-2}{5} \), which is consistent with the slope from the equation.

Since both the slope and y-intercept match the function, we conclude that the given graph corresponds to the function \( y = -\frac{2}{5}x + 3 \).

Thus, the answer is:

1 (for yes).