Question

Find the equation for the horizontal line that goes through point V(-5,17).

Answer 1

x=-5

Explanation:

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Answer 2

`y = 17`.

Explanation:

In general, the equation of a line in a cartesian plane may be written as
`y = m\, x + b`, where
`m` and
`b` are constants:
`m\!` is the slope of this line, and
`b\!` is the
`y`-intercept of this line.

A point
`(x_(0),\, y_(0))` is on a given line if and only
`x := x_(0)` and
`y := y_(0)` (setting
`x` to
`x_(0)` and
`y` to
`y_(0)`) would satisfy the equation of that line.

That is:
`y_(0) = m\, x_(0) + b`.

A line in a cartesian plane is horizontal if and only if its slope is
`0`. That is:
`m = 0`. The equation of this line would be in the form
`y = b` for some constant
`b`.

The point
`(-5,\, 17)` is on the line in this question. Thus,
`x := -5` and
`y := 17` should satisfy the equation of this line. That is:
`17 = b`.

Hence, the value of the constant
`b` would be
`17` for this particular line. The equation of the line would be
`y = 17`.