Question

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 7 to 7 in one unit increments. An upward slanting line is graphed on the coordinate plane. The line passes through points plotted at left parenthesis negative 6 comma negative 1 right parenthesis, left parenthesis 0 comma 0 right parenthesis, and left parenthesis 6 comma 1 right parenthesis.

Determine if the given graph is the graph of the function y=16x
. Enter 1 for yes. Enter 2 for no.

(1 point)

Answer 1

To determine if the graph is that of the function \( y = 16x \), we need to analyze the characteristics of the line described in your question.

The line passes through the points:

• \((-6, -1)\)
• \((0, 0)\)
• \((6, 1)\)

Let’s check the slope of the line formed by these points.

1. Calculate the slope:

   • The slope \( m \) is calculated as \( m = \frac{y_2 - y_1}{x_2 - x_1} \).
   • Using the points \((0,0)\) and \((6,1)\): \[ m = \frac{1 - 0}{6 - 0} = \frac{1}{6} \]

2. Now, the function \( y = 16x \) has a slope of 16. Since the calculated slope of the line is \( \frac{1}{6} \), which is not equal to 16, the line described in the image does not match the equation \( y = 16x \).

Thus, the answer is:

2 (no).