Emily designed a robot that could climb down steps. She drew a graph to show the results from a test of her new robot. The graph shows the number of steps remaining over time.

Question

Which equation represents Emily’s situation, where x is the number of seconds and y is the number of steps?

Responses

y=−110x+15
y equals negative fraction 1 over 10 end fraction x plus 15

y=−10x+150
y equals negative 10 x plus 150

y = 10x + 150
y = 10 x + 150

y=110x+15
y equals fraction 1 over 10 end fraction x plus 15
First quadrant grid, x-axis numbered 0 to 150 and labeled Seconds, y-axis numbered 0 to 19 and labeled Steps. A line with negative slope intersects the y-axis at 15 and the x-axis at 150.

Answer 1

To determine which equation represents Emily's robot situation, we can analyze the details provided about the graph:

1. The graph has a negative slope, indicating that as time (in seconds, represented by \(x\)) increases, the number of steps remaining (represented by \(y\)) decreases.

2. The y-intercept is given as 15, which means that when \(x = 0\) (at time zero), the number of steps remaining is 15.

3. The graph also intersects the x-axis (where \(y = 0\)) at \(x = 150\). This indicates that after 150 seconds, there are no steps remaining.

Given that information, we can set up the slope and intercept:

• The slope (\(m\)) can be calculated as the change in \(y\) divided by the change in \(x\) between the two intercepts:

  \[ \text{slope} = \frac{\Delta y}{\Delta x} = \frac{0 - 15}{150 - 0} = \frac{-15}{150} = -\frac{1}{10} \]

• The equation in slope-intercept form \(y = mx + b\) can thus be represented as:

  \[ y = -\frac{1}{10}x + 15 \]

With that in mind, we look at the provided equations. The correct equation that matches our findings is:

y = -\frac{1}{10}x + 15

This is represented in the options as:

y=−\frac{1}{10}x+15

This corresponds to the situation described for Emily's robot.