Question

Goal F: I can write an equation from two points.

Write an equation of the line that passes through the points given.
8. (1,5) and (4, -2)
9. (2, -1) and (-5,-5)
10.
(0,3) and (4,0)​

Answer 1

8.
`y=-(7)/(3)(x-1)+5`

9.
`y=(4)/(7)(x-2)-1`

10.
`y=-(3)/(4)x+3`

Explanation:

The equation of a line passing through points
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is given as:

`y-y_(1)=((y_(2)-y_(1))/(x_(2)-x_(1)))(x-x_(1))`

For #8:

`(x_(1),y_(1))` is
`(1,5)` and
`(x_(2),y_(2))` is
`(4, -2)`.

Now, plug in these values and find the equation of the line. This gives,

`y-5=((-2-5)/(4-1))(x-1)\\y-5=((-7)/(3))(x-1)\\y=-(7)/(3)(x-1)+5`

Therefore, the equation of a line passing through
`(1,5)` and
`(4, -2)` is
`y=-(7)/(3)(x-1)+5`.

For #9:

`(x_(1),y_(1))` is
`(2,-1)` and
`(x_(2),y_(2))` is
`(-5, -5)`.

Now, plug in these values and find the equation of the line. This gives,

`y-(-1)=((-5-(-1))/(-5-2))(x-2)\\y+1=(-5+1)/(-7)(x-2)\\y+1=((-4)/(-7))(x-2)\\y=(4)/(7)(x-2)-1`

Therefore, the equation of a line passing through
`(2,-1)` and
`(-5, -5)` is
`y=(4)/(7)(x-2)-1`.

For #10:

`(x_(1),y_(1))` is
`(0,3)` and
`(x_(2),y_(2))` is
`(4, 0)`.

Now, plug in these values and find the equation of the line. This gives,

`y-3=((0-3)/(4-0))(x-0)\\y-3=((-3)/(4))(x)\\y=-(3)/(4)x+3`

Therefore, the equation of a line passing through
`(0,3)` and
`(4, 0)` is
`y=-(3)/(4)x+3`.