Question

What is the equation of the line that contains the points with (x, y) coordinates (-3, 7) and (5, -1)?

Answer 1

`x+y=4`

Explanation:

If `(x_1,y_1)=(-3,7)` and `(x_2,y_2)=(5,-1)` are points on a straight line, then the slope of that line is
`color(white)("XXX")m=(y_2-y_1)/(x_2-x_1)=(-1-7)/(5-(-3))=(-8)/8=-1`

Any general point `(x,y)` on this line together with `(x_1,y_1)=(-3,7)`, for example must have this same slope"
`color(white)("XXX")(y-y_1)/(x-x_1)=-1`
or
`color(white)("XXX")(y-7)/(x-(-3))=-1`

Simplifying further
`color(white)("XXX")y-7=(-1) * (x+3)`

`color(white)("XXX")y-7=-x-3`

In standard form:
`color(white)("XXX")x+y=4`