Determine if the relationship represented in the table is linear. If it is linear, write an equation.
how do you determine if a table is linear here is the table I am looking at....
x 2 5 7 10 12 20
y -3 0 2 5 7 15
please guide me in the right direction...
pick a delta x. Say from 2to 5,or a deltax of 3
Notice the corresponding delta y is -3 to 0, a deltay of 3
slope= deltaty/deltax= 3/3=1
Now try it for other pairs.
7 to 10 would then be 3 and 2 to 5 is also 3 and then the last would be 12 to 20 would be 8 and 7 to 15 would be 8 so this would be a linear but then how do you write an equation?
y= mx+b
you know m as 1.
y= x+b
now put in any x,y pair, and solve for b.
y=1(3/8)+3?? is that right?
No. y=x+b
2=7+b
7-2=b I think you can get it from here :)
To determine if a table represents a linear relationship, you need to check if there is a constant rate of change between the x-values and y-values. If there is a consistent change in y for every unit increase in x, then the relationship is linear. Here's how you can check it:
Step 1: Calculate the difference between consecutive x-values and y-values.
x-values: 5-2 = 3, 7-5 = 2, 10-7 = 3, 12-10 = 2, 20-12 = 8
y-values: 0-(-3) = 3, 2-0 = 2, 5-2 = 3, 7-5 = 2, 15-7 = 8
Step 2: Examine the differences in the x-values and y-values.
The differences in the x-values are not constant. For example, the difference between 7 and 5 is 2, and the difference between 10 and 7 is 3. Therefore, the x-values do not have a constant rate of change.
Similarly, the differences in the y-values are also not constant. For instance, the difference between 2 and 0 is 2, but the difference between 7 and 5 is 2. Hence, the y-values do not have a constant rate of change.
Since both the x-values and y-values do not have a constant rate of change, the relationship represented in the table is not linear. Therefore, we cannot write a linear equation for this table.