Question

If you had the points (4, -8) and (-7, 3) how would you find the equation of the line. I don’t know how to find the y-intercept but I know how to find x

Answer 1

`y=-x-4`

where the y-intercept is (0, -4).

Step-by-step explanation

The equation of the line can be given in the slope-intercept form:

`y=mx+b`

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

The slope m can be calculated with the following formula:

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

As we are given two points, (4, -8) and (-7, 3), we can replace the values as follows and simplify:

`m=(3-(-8))/(-7-4)`
`m=(3+8)/(-7-4)`
`m=(11)/(-11)=-1`

Thus, our slope is:

`y=(-1)\cdot x+b`
`y=-x+b`

Then, we can replace any of the points given in the equation to find the y-intercept. For example, choosing (4, -8):

`-8=-(4)+b`
`-8=-(4)+b`

Solving for b :

`-8=-4+b`
`-8+4=b`
`-4=b`
`b=-4`

Finally, our equation is:

`y=-x-4`