Use the image to answer the question.

Question

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.

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

(1 point)

Answer 1

To determine if the given graph represents the function \( y = -\frac{2}{5}x + 3 \), we can analyze the equation and the coordinates of the points it passes through.

1. Identify the slope (m): The slope of the line represented by the equation \( y = -\frac{2}{5}x + 3 \) is \( -\frac{2}{5} \). This indicates that for every 5 units you move to the right on the x-axis, you move 2 units down on the y-axis, which means the line is slanting downwards.

2. Identify the y-intercept (b): The y-intercept of the line is 3, meaning it passes through the point (0, 3).

3. Check the second point (5, 1): Now, we need to check if when \( x = 5 \), \( y \) equals 1 in our function: \[ y = -\frac{2}{5}(5) + 3 = -2 + 3 = 1. \] This confirms that when \( x = 5 \), \( y = 1 \), which means the line does pass through the point (5, 1).

Since the line correctly passes through both points (0, 3) and (5, 1), we can conclude that the given graph is indeed the graph of the function \( y = -\frac{2}{5}x + 3 \).

Thus, the answer is 1 for yes.