x y 0 3 3 9 6 15 10 23 Which of the following linear equations corresponds to the table above?

Answer 1

I am assuming here that the table in question is the following:

x	y
0	3
3	9
6	15
10	23

You only need two of those points in order to come up with the equation of the corresponding line.

We’ll solve the problem in 2 ways

1. Solution in y-intercept form  y=mx+b

We can calculate the slope of the line using any 2 of the given points: I pick (0,3) and (3,9) . Recall the formula for finding the slope of the line through 2 points (x1,y1) and (x2,y2) as m=(y2-y1)/(x2-x1)

By plugging in the corresponding values, we get  (9-3)/(3-0)=6/3=2

Since we now the value of y when x is zero, i.e. the point (0,3) of the table, then the value of b is 3.

Now, putting everything together, we have y=2x+3

2. Solution in point-slope form y-y1=m(x-x1)

You can proceed the same way above to find the slope m=2

Now use one of the points in the given table to plug into x1 and y1

Doing the last 2 steps will result in y-23=2(x-10) if you use the point (10,23)

Realize that the point slope form of the equation of a line is not unique since using a different point will result in different values of x1 and y1. That said y-3=2(x-0) would also be a valid answer in the point-slope form.