Question

What linear equation in slope intercept from does this graph represent?​

Answer 1

`y = 16(2)/(3) x + 100` or
`y = (50)/(3) + 100`

Explanation:

The equation of a line is
`y = mx + b`, with
`m` being the slope and
`b` being the y-intercept.

We can see on the graph that the y-intercept, where the line crosses or touches the y-axis, is 100. So, our new equation is
`y = mx + 100`.

Now we have to find the slope. Let's pick a point that's clearly on the graph. Perhaps (3, 150). And then we'll take the y-intercept point for convenience, (0, 100).

Then, we'll use
`(y_(2) - y_(1))/(x_(2) - x_(1) )` to find the slope.

Let's substitute in our points.

`(150-100)/(3-0)`

Simplify.

`(50)/(3)`

Now, we can leave the slope like that or turn it into a mixed number. As a mixed number, your slope is
`16(2)/(3)`.

We'll put that in our equation for a line and...bam!

`y = 16(2)/(3) x + 100` or
`y = (50)/(3) + 100`