Use the image to answer the question

Question

A coordinate plane ranges from negative 9 to 9 in unit increments on the x-axis and from 11 to negative 11 in unit increments on the y-axis. A line with arrows at both the ends joins two plotted points and extends beyond. The coordinates of the plotted points are: left parenthesis 0 comma 0 right parenthesis and left parenthesis 5 comma 1 right parenthesis.

Is this the correct graph of the equation y=15x ?

Answer 1

To determine if the graph described matches the equation \( y = 15x \), we can analyze the points given.

1. Verify the Points Against the Equation:

   • The first point is \( (0, 0) \): \[ y = 15(0) = 0 \] This point satisfies the equation.

   • The second point is \( (5, 1) \): \[ y = 15(5) = 75 \] This point does not satisfy the equation since \( 1 \neq 75 \).

2. Slope Analysis: The slope of the line described by the two points can also be calculated:

   • With points \( (0, 0) \) and \( (5, 1) \), the slope \( m \) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{5 - 0} = \frac{1}{5} \]
   • The slope of the line given by the equation \( y = 15x \) is \( 15 \).

Since the slope calculated from the two points \( (0, 0) \) and \( (5, 1) \) is \( \frac{1}{5} \) and not \( 15 \), the line represented by these points does not correspond to the equation \( y = 15x \).

Thus, the graph is not the correct graph of the equation \( y = 15x \).

Answer 2

Yes, it is the correct graph because the slope =5/1.

No, it is not the correct graph because the slope m=riserun=1/5.

Yes, it is the correct graph because the ordered pair (0, 0) satisfies the equation and the slope m=rise/run=1/5.

No, it is not the correct graph because the ordered pair (1, 5) is not a point on the graph of y=1/5 x

Answer 3

Given your statement, let's clarify the logical evaluations based on the points and the equation, \( y = 15x \).

1. Evaluating the Points:

   • The first point \( (0, 0) \) satisfies \( y = 15(0) = 0 \), which is correct.
   • The second point \( (5, 1) \):
     \[ y = 15(5) = 75 \quad \text{(not equal to 1)} \]

2. Determining the Slope:

   • You correctly noted the calculation: \[ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{1 - 0}{5 - 0} = \frac{1}{5} \]

3. Comparison with the Given Equation:

   • The slope calculated (\( \frac{1}{5} \)) does not match the slope of the line represented by \( y = 15x \), which has a much steeper slope of \( 15 \).
   • The correct slope for the line through \( (0, 0) \) and \( (5, 1) \) indicates that if this was part of a linear relationship, it would represent a different equation, specifically \( y = \frac{1}{5}x \), not \( y = 15x \).

Conclusion:

The correct evaluation based on the provided initial assertion is:

No, it is not the correct graph because the slope \( m = \text{rise/run} = \frac{1}{5} \), which does not match the slope of the equation \( y = 15x \).

The potential correction considering the slope \( \frac{1}{5} \) aligns with the linear equation \( y = \frac{1}{5}x \), not \( y = 15x \). Therefore, the conclusion remains that it is not the correct graph of \( y = 15x \).