Question

Question #8a759

Answer 1

a. `y=-2`
b. `y=2x-3`
c. `y=5`

Explanation:

For a., a horizontal line means that the line has a zero slope and thus the equation for this line is `y=-2`

For b., you must use the point-slope formula: `y-y_1=m(x-x_1)`
Since the line must be parallel to the line `2x+3`, our slope (or `m`) has to be the same as the equation just mentioned: `2`. In addition we are given the point `(5,7) -> (x_1,y_1)`

We can now substitute for the point-slope formula:

`y-7=2(x-5)`

`y-7=2x-10`

We can rewrite the equation in `y=mx+b` form by adding `7` to both sides.

`ycancel(-7+7)=2x-10+7`

`y=2x-3`

For c.

First we find the slope using: `m=(y_2-y_1)/(x_2-x_1)`

We know that:
`(-3,5)->(x_1,y_1)`
`(2,5)-> (x_2,y_2)`

Thus:

`m=(5-5)/(2-(-3))=0/5=0`

`m=0`

Now we can use the point slope formula to find the equation for this line using our newly found `m` and any of the two points given. I will use `(2,5)`

`y-5=0(x-2)`

`y-5=0`

In `y=mx+b` form, we add `5` to both sides

`ycancel(-5+5)=0+5`

`y=5`