Question

One of the tables below contains (x, y) values that were generated by a linear function. Determine which table, then write the equation of the linear function represented by the table. One of the tables below contains (x, y) values that were generated by a linear function. Determine which table, then write the equation of the linear function represented by the table.

I know the equation; y = 2.5x - 4, and I know that table 3 is the correct answer, but I don't understand how they got the answer... Can someone explain it for me?

Answer 1

Linear motion implies that there is a steady slope (or rate of change). Table three is the only one where the y values go up by 5 each time.

You know that y = 2.5x - 4 is the answer, so you know the slope is 2.5. This means that for every 1 x, you go up 2.5 y. Since the table shows values of x going up by two, y is going up by double 2.5, which is 5.

Answer 2

Is there a way to write this is an equation?
I've tried doing the point slope form, then once I get the slope I find the intercept... but I never get the same equation that I was given.

Answer 3

If we use the first point as an example, (2,1)

Recall that point slope form is written y - y1 = m(x - x1) where x1 = 2, y1 = 1

Substituting in, we get y - 1 = 2.5(x - 2)

If you simplify that further, you should get y = 2.5x - 4

Answer 4

>o< I kept mixing my x and y's up... I wrote them down like that but once I plugged them into the equation I mixed 'em up. . .

Thank yhu for the help. I appreciate it. =^.^=