For chemistry, I have to make a line graph. My teacher specifically instructed us to make one with smooth, fluid lines, not with choppy ones, so it would form a curve. I am suppposed to find the slope of the line, but I don't know how to, because the line goes up and down and up and down. Should I just simply input the first point, and the last point? Or should I find the slope for each individual segment? Thanks, Coralie.

Question

For chemistry, I have to make a line graph. My teacher specifically instructed us to make one with smooth, fluid lines, not with choppy ones, so it would form a curve. I am suppposed to find the slope of the line, but I don't know how to, because the line goes up and down and up and down. Should I just simply input the first point, and the last point? Or should I find the slope for each individual segment? Thanks, Coralie.

Answer 1

Personally, I would simplify my diagram if the teacher didn't specify how much it was to go up and down and draw a smooth curve something on the order of a semicircle, or parabola, then find the slope at two or three places along the curved line.

Answer 2

To find the slope of your line graph, you will need to calculate the slope for each individual segment. Since the line goes up and down, you will have multiple linear segments instead of a single straight line.

Here is how you can do it:

1. Identify each segment of the line graph where the line is continuous and smooth. These segments should have clear directionality, either increasing or decreasing.

2. Select two points on each segment that you want to calculate the slope for. Choose points that are evenly spaced and give you a good representation of the trend in that segment.

3. Use the formula for slope, which is defined as the change in the y-values divided by the change in the x-values:

Slope = (change in y) / (change in x)

Calculate the change in y by subtracting the y-coordinate of the first point from the y-coordinate of the second point. Do the same for the change in x, subtracting the x-coordinate of the first point from the x-coordinate of the second point.

4. Divide the change in y by the change in x to calculate the slope for that segment. This will give you the instantaneous rate of change for that specific portion of the line graph.

5. Repeat this process for each segment of the line graph, calculating the slope for each one.

By finding the slope for each individual segment, you can accurately represent the changing trends of your line graph and achieve the smooth, fluid curves that your teacher has instructed you to create.