Answer:
Step 1: First, focus on one column and pick two points in the table to calculate slope. Plot these points on a graph with Cartesian coordinates. If we wanted to do Points 3 and 7 for example, we would plot them on the graph like so:
Point#3 = (-2,-5) Point#7 = (1,-10)
Step 2: Next, find the difference in y-coords between each pair of data points by subtracting Column#3's value from Column#7's value when you are looking at Point#3:-5 - 10= -15 OR when you are looking at Point #7 10- -2=-18. This tells us that in this instance the slope is negative.
Step 3: Then, take the difference between Column#1's value and Column #3's value when you are looking at Point#3:-5 - (-2)=7 OR when you are looking at Point #7(-10)-(1)=-9 This tells us that in this instance the slope is positive.
We can do this for any two points of data to find the two slopes.
Once we have found all our slopes, we can use our table of values to set up an equation y=mx+b where m=gradient (m=slope=rise/run) x = First number in ordered pair b = y-intercept (the second number in an ordered pair) With this equation we can use our points 3 and 7 to find their corresponding y-intercepts, which are -15 and -18. Once you have found the y-intercepts, you can plug in any x-value into your equation with m & b to see what the corresponding y value will be! For example:
Once you've done this for each ordered pair, plot them on a graph if possible, otherwise make sure they are all in order. Below is what they should look like once plotted on an xy scatter plot (ignore the fact that I did my line backwards in some parts of it):
The red line is positive slope while the blue line is negative slope. The green line was not included in the table of values. You can see that it looks very similar to the red line, but doesn't intersect some points on the x axis. This is because we set our gradient (m) to be negative and so it had to curve downwards instead of upwards like a positive angle would:
This means that while the red and blue lines cross more often than they don't, this green line will only ever cross up once! It is simply their "mirror image". That's why when you shift your graph, this green line still behaves exactly as it did before. If you shift your graph for this problem by 3 units in an upwards direction, all you have to do is change -3's to +3's for both m & b to get the same graph as before!
**ANSWER MADE BY AN AI**
is the constant of proportionality