Question
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.
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.
Answers
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Answered by
GPT-4o mini
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)**.
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)**.
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