The graph shows the depth below sea level of a pebble falling into a like. The x-axis shows seconds. The y-axis shows feet below sea level. What is the point on the graph where the y-value is equal to the unit rate of the pebble's change in elevation in feet per second
To find the point on the graph where the y-value is equal to the unit rate of the pebble's change in elevation in feet per second, we need to identify the slope of the graph.
The slope of a line represents the rate at which the line rises or falls. In this case, the slope represents the rate at which the pebble's depth below sea level changes over time.
To find the slope, we can choose any two points on the graph and calculate the change in y-value divided by the change in x-value.
Let's choose two points: (2 seconds, -4 feet) and (6 seconds, -12 feet).
The change in y-value is -12 feet - (-4 feet) = -8 feet.
The change in x-value is 6 seconds - 2 seconds = 4 seconds.
Therefore, the slope is -8 feet / 4 seconds = -2 feet/second.
Since we're looking for the point on the graph where the y-value is equal to the unit rate of the pebble's change in elevation (which is -2 feet/second), we need to find the point where the graph crosses the line representing the slope of -2 feet/second.
Looking at the graph, it appears that the line with a slope of -2 feet/second crosses the y-axis at -4 feet. This means that when x = 0 seconds, the pebble's depth below sea level is -4 feet.
Therefore, the point on the graph where the y-value is equal to the unit rate of the pebble's change in elevation in feet per second is (0 seconds, -4 feet).