What is the slope of the line represented by the points in the table?
mc016-1.jpg
Negative 0.05
Negative .005
0.005
0.05
Negative 0.05
Raj is deciding between two cell phone plans, A and B, which are both linear functions. The monthly charge for plan A according to the number of minutes used is shown in the table.
Monthly Charge for Plan A
Minutes used, x
Monthly charge ($), y
0
14.45
3
14.84
6
15.23
9
15.62
12
16.01
Plan B has the same monthly base charge as plan A, but it charges a different amount per minute used. If the total monthly charge for plan B is $22.10 when 45 minutes are used, what is the slope of the linear function that represents the cost of plan B?
0.13
0.17
0.39
0.45
First, we need to find the monthly base charge for plan A by looking at the table. It is $14.45.
Next, we can use the point-slope formula to find the slope of the linear function that represents the cost of plan B:
slope = (y2 - y1) / (x2 - x1)
We can choose any two points from the table for this calculation, but let's use (0, 14.45) and (45, 22.10) since we know the total monthly charge for plan B when 45 minutes are used.
slope = (22.10 - 14.45) / (45 - 0)
slope = 7.65 / 45
slope = 0.17
Therefore, the slope of the linear function that represents the cost of plan B is 0.17.
Ellen thinks that if a line has no slope, then it never touches the y-axis. Which line proves that her statement is incorrect?
x = 0
y = 0
x = 1
y = 1
The line that proves Ellen's statement incorrect is: x = 0.
This is a vertical line that intersects the y-axis at the point (0, y) for any value of y. Since the slope of a vertical line is undefined, Ellen's statement would imply that this line never touches the y-axis, but in fact, it intersects the y-axis at every point.
What is the slope of the line in the graph?
On a coordinate plane, a line goes through points (negative 2, negative 1) and (0, 1).
The slope of a line going through points (x1, y1) and (x2, y2) is given by:
slope = (y2 - y1) / (x2 - x1)
In this case, we can use the points (-2,-1) and (0,1):
slope = (1 - (-1)) / (0 - (-2))
slope = 2 / 2
slope = 1
Therefore, the slope of the line in the graph is 1.