Use the image to answer the 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)

1 answer

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).

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