Question

Find the equation of the linear function represented by the table below in slope-intercept form.

Answer 1

y=-2x+3

Explanation:

Use the slope formula

`m=(y_(2)-y_(1) )/(x_(2)-x_(1) )`

According to the table, x=1 and y=1. There is another point x=2 and y=-1.

We can say that
`x_(1)=1` and
`y_(1) =1`. We can also say that
`x_(2)=2` and
`y_(2)=-1`. Plugging this into the equation we get:

`m=(-1-1)/(2-1)=-2`.

This means that the slope of your equation is -1/2

Point intercept form is y=mx+b

So plugging the slope in we have
`y=2x+b`

We can plug in one of the values from the value table for x and y, but to keep things simple, I’m going to just use x=1, and y=1, the first values on the table. Plugging these into the equation we get:

`1=-2(1)+b\\ 1=-2 +b\\b=1+2 \\b=3`

So our equation is
`y=-2x+3`