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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)
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1 answer

To determine if the given graph corresponds to the function \( y = -25x + 3 \), we can check the slope and y-intercept of the line based on the plotted points \( (0, 3) \) and \( (5, 1) \).

  1. Identify the y-intercept: The y-intercept is the value of y when x = 0. From the point \( (0, 3) \), we see that the y-intercept is indeed 3.

  2. Calculate the slope (m): The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \( (0, 3) \) and \( (5, 1) \), we have: \[ m = \frac{1 - 3}{5 - 0} = \frac{-2}{5} \] This means the slope of the line represented by these points is \( -\frac{2}{5} \).

  3. Compare the slope with the given equation: The given line \( y = -25x + 3 \) has a slope of \(-25\), which is different from \(-\frac{2}{5}\).

Since the slopes do not match, the given graph does not represent the function \( y = -25x + 3 \).

Therefore, the answer is 2 (no).