Question

Question #ad1ea

Answer 1

`f=0`

Explanation:

.

The equation of a straight line is in the form of:

`y=mx+b`

where `m` is the slope and `b` is the `y`-intercept.

Therefore, the equation of this line can be written as:

`y=10x+b`

We can solve for `b` by using the coordinates of a point on the line:

`2=10(1)+b`

`b=-8`

Therefore, the equation is:

`y=10x-8`

Now, we can plug in the coordinates of the other point and solve for `f`:

`-8=10(f)-8`

`10f=0`

`f=0`

Answer 2

`f = 0`

Explanation:

The slope is figured from this formula:

`m` (the slope) = `(y_2 - y_1)/(x_2 - x_1)`

This is a formula with 5 unknowns, but you have been given 4 of them.

Let the point `(x_1,y_1)` be the given point `(1,2)`
Then the point `(x_2,y_2)` is `(f,`-`8)`.

So of the 5 unknowns, you know four of them:
`m` . . . . . `10`
`y_2` . . . .`-  8`
`y_1` . . . . . . `2`
`x_1` . . . . . . `1`
`x_2` . . . . . . .`f` -- Find `f`

Sub in the known values in the place of their letters
and solve the slope equation for `f`

`m` = `(y_2−y_1)/(x_2−x_1)`

`10 = ((-8 - 2))/((f - 1))`
Solve for `f`

1) Combine like terms
`10 = (-10)/((f-1))`

2) To get `f` out of the denominator, multiply both sides by `(f-1)` and let the denominator cancel
`10(f-1) = -10`

3) Divide both sides by `10`
`f - 1 = -1`

4) Add 1 to both sides to isolate `f`
`f = 0` `larr` answer

Answer:
`f = 0`

Check
Sub in `0` for `f` in the original equation and see if it equals `10`
`(y_2−y_1)/(f−x_1)` should equal `10`

`(-8−2)/(0−1)` should equal `10`

`(-10)/(-1)` should equal `10`

`10` does equal `10`

`Check!`