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=−25x+3
. Enter 1 for yes. Enter 2 for no.

(1 point)

Answer 1

To determine if the graph of the function \( y = -25x + 3 \) matches the line illustrated in the given description, we can analyze the function itself.

The function is in the slope-intercept form \( y = mx + b \), where:

• \( m = -25 \) (the slope)
• \( b = 3 \) (the y-intercept)

The slope of \(-25\) indicates that for every unit increase in \( x \), \( y \) decreases by \( 25 \). This creates a very steep line descending sharply from left to right.

Next, let's evaluate the two points mentioned:

• The point \( (0, 3) \) corresponds to the y-intercept of the function, which is correct.
• At \( x = 5 \), we substitute \( x \) into the function:

\[ y = -25(5) + 3 = -125 + 3 = -122 \]

The point \( (5, 1) \) mentioned in the description does not satisfy the equation \( y = -25x + 3 \), as substituting \( x = 5 \) gives \( y = -122 \), not \( 1 \).

Since the line cannot pass through both \( (0, 3) \) and \( (5, 1) \) for the equation \( y = -25x + 3 \), we conclude that the given graph is not the graph of the function.

Thus, the answer is:

2 (no).