x y
-2 80
-1 70
2 40
5 10
Answer the questions using the table.
(3 points)
the rate of change =
the y−intercept =
the equation of the line is
To find the rate of change, we can compare the change in y-values with the change in x-values.
From x = -2 to x = 5, the change in x is 5 - (-2) = 7.
From y = 80 to y = 10, the change in y is 10 - 80 = -70.
Therefore, the rate of change is -70/7 = -10.
To find the y-intercept, we can look at the point where the line crosses the y-axis. In this case, the y-intercept is the value of y when x = 0. Looking at the table, we can see that there is no data point for x = 0. Therefore, we cannot determine the y-intercept from the given table.
However, we can determine the equation of the line using the point-slope form. We know the rate of change is -10, and let's choose the point (2, 40) to plug into the equation.
Using the point-slope form: y - y1 = m(x - x1), where m is the rate of change and (x1, y1) is the given point, we have:
y - 40 = -10(x - 2)
Expanding the equation:
y - 40 = -10x + 20
Rearranging:
y = -10x + 60
Therefore, the equation of the line is y = -10x + 60.
u sure
Apologies for the confusion in my previous response. Let's reassess the table to correctly answer the questions.
The rate of change can be found by comparing the change in y-values with the change in x-values. From x = -2 to x = -1, the change in x is -1 - (-2) = 1. From y = 80 to y = 70, the change in y is 70 - 80 = -10. Therefore, the rate of change is -10/1 = -10.
The y-intercept is the value of y when x = 0. Looking at the table, we don't have a data point for x = 0, so we cannot determine the y-intercept.
Without the y-intercept, we cannot determine the equation of the line with absolute certainty. However, based on the available data points, we can calculate the slope as -10 and write the equation of the line in slope-intercept form using one of the points. Let's use the point (-2, 80).
Using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept, we have:
80 = -10(-2) + b
80 = 20 + b
b = 60
So, based on the available data points, the equation of the line is y = -10x + 60.