Question

How do you write an equation of a line that contains (5, 7) and (-3, 11)?

Answer 1

`x+2y=19`

Explanation:

The slope of a line through `(5,7)` and `(-3,11)` is given by the relation:
`color(white)("XXX")color(green)m=(Deltay)/(Deltax)=(11-7)/((-3)-5)=color(green)(-1/2)`

The slope-point form for a line with slope `color(green)m` through a point `(color(red)a,color(blue)b)` is
`color(white)("XXX")y-color(blue)b=color(green)m(x-color(red)a)`

Using `color(green)(m=-1/2)` as the slope and
`(color(red)a,color(blue)b)=(color(red)5,color(blue)7)` as a point,
we have:
`color(white)("XXX")y-color(blue)7=color(green)(-1/2)(x-color(red)5)`

While this could be considered a valid solution to the given question,
it is normal to convert this into standard form:

`color(white)("XXX")2y-14=-x+5`

`color(white)("XXX")x+2y=19`