Question

Find the following equation

Answer 1

`y=(-1)/(2)x+7`

Explanation:

Slope intercept form:
`y=mx+b` when
`m` is the slope of the line and
`b` is the y-intercept (the y-coordinate of the point the line crosses the y-axis)

1) Find the slope (
`m`)

`m=(y_2-y_1)/(x_2-x_1)` when the points are
`(x_1,y_1)` and
`(x_2,y_2)`

We can use any two points that the table gives us to plug into this equation. For example, we can use the points (14,0) and (0,7):

`m=(0-7)/(14-0)\\m=(-7)/(14)`

Simplify the fraction

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

So far, our equation looks like this:

`y=(-1)/(2)x+b`

2) Find the y-intercept (
`b`)

The y-intercept is the y-coordinate of the point the line crosses the y-axis, or in other words, it's the value of y when x is equal to 0.

Looking at the table, we can see that y is equal to 7 when x is equal to 0, so, therefore,
`b=7`.

Now, this is our final equation after plugging in
`m` and
`b`:

`y=(-1)/(2)x+7`

I hope this helps!