The cost, (x) for a taxi is given by c (x) = 2x + 4.00, where x is the number of minutes. What does the slope mean for this situation?
The taxi ride costs a total of $4.00.
The rate of change of the cost of the taxi ride is $4.00 per minute.
The rate of change of the cost of the taxi ride is $2.00 per minute.
The taxi ride costs $2.00 per trip.
The correct answer is: The rate of change of the cost of the taxi ride is $2.00 per minute.
The slope in this situation represents the rate of change of the cost of the taxi ride per minute. Since the formula for the cost is c(x) = 2x + 4.00, the coefficient of x (2) represents the rate of change. This means that for each additional minute, the cost of the taxi ride increases by $2.00.
Do you know how to find the slope of a graph?
Yes, the slope of a graph can be found by calculating the change in y-coordinates divided by the change in x-coordinates between two points on the graph.
More formally, the slope of a line can be calculated using the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
This is also known as rise over run.
Another way to find the slope of a linear equation in the form y = mx + b, where m is the slope, is to take the coefficient of x. The coefficient of x represents the rate of change of y with respect to x.
Do you know how to find the slope of a graph when one number is negative?
Yes, when calculating the slope of a graph with one of the numbers being negative, you would still use the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
If one of the y-coordinates is negative, it simply means that the line on the graph is decreasing instead of increasing. The slope will also be negative in this case.
For example, if you have two points (x1, y1) and (x2, y2) and the y-coordinates are -4 and 2 respectively, the change in y-coordinates would be:
change in y-coordinates = 2 - (-4) = 2 + 4 = 6
And if the x-coordinates are 3 and 5, the change in x-coordinates would be:
change in x-coordinates = 5 - 3 = 2
Therefore, the slope would be:
slope = 6 / 2 = 3
In this case, the slope would be positive, indicating that the line is increasing as x increases.
Put it in a way a 5th grader understands please, thanks. I'm not in 5th grade I just need u do explain it simpler plz.
Of course! Imagine you have a line on a graph that goes from a point with a y-value of -2, down to a point with a y-value of -6.
To find the slope, you look at how much the y-values change. In this case, the y-value changed from -2 to -6.
So, the change in y-coordinates is -2 (start) - (-6) (end), which can be written as -2 + 6 = 4.
Next, you look at how much the x-values change. If the x-values are going from 3 to 5, the change in x-coordinates is 5 - 3 = 2.
Then, you just divide the change in y-coordinates by the change in x-coordinates to find the slope: 4 / 2 = 2.
So, in this case, the slope is 2. The negative sign in front of the 2 would indicate that the line is going downwards on the graph as you move from left to right.
I hope that explanation was helpful in simpler terms!
So if u go up 2, run 4 thatll get you to 6? Is that hw you got it?
Yes, that's correct! Another way to think about it is using "rise" and "run" to understand slope.
In this case, the slope is 2. This means that for every 4 units you move to the right (run), you go up 2 units (rise) on the graph.
So, if you start at the point (-2, 3) and move 4 units to the right, you would end up at the point (2, 5) since you went up 2 units at a rate of 2/4 (slope).
I hope this explanation clarifies things further for you!