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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 answer

To determine if the graph represents the function \( y = -25x + 3 \), we need to examine the characteristics of this linear equation and compare it with the points provided in the question.

  1. The equation \( y = -25x + 3 \) has a slope of -25, which indicates that for every unit increase in \( x \), \( y \) decreases by 25 units. This is a very steep downward-slanting line.

  2. Now let's check the two points mentioned in the question:

    • The first point is \( (0, 3) \): Substituting \( x = 0 \) into the equation: \[ y = -25(0) + 3 = 3 \] Therefore, the point \( (0, 3) \) lies on the line.

    • The second point is \( (5, 1) \): Substituting \( x = 5 \) into the equation: \[ y = -25(5) + 3 = -125 + 3 = -122 \] Therefore, the point \( (5, 1) \) does NOT lie on the line, since the calculation shows \( (5, -122) \).

Since one of the points provided does not lie on the line \( y = -25x + 3 \), we can conclude that the given graph does not represent that function.

The answer is: 2 (no).