Question

What is the equation of the line that passes through the point

(
1
,
3
)
(1,3) and has a slope of
−
3
−3?

Answer 1

The line
`y = -3\, x + 6` goes through the point
`(1,\, 3)` and has a slope of
`(-3)`.

Explanation:

If the slope of a line is
`m` and the
`y`-intercept of that line is
`b` (
`m\!` and
`b\!` are constants), then
`y = m\, x + b` would be the slope-intercept equation of that line.

The slope of the line in this question is
`m = -3`. However,
`b`, the
`y`-intercept of this line, still needs to be found. The equation of this line would be
`y = -3\, x + b` for some constant
`b\!`.

Since this line goes through
`(1,\, 3)`,
`x = 1` and
`y = 3` should satisfy the equation of this line. In other words, if
`x = 1\!` and
`y = 3\!` are substituted into
`y = -3\, x + b`, the result should still be an equality:

`3 = -3* 1 + b`.

Solve this equation for
`b`:

`b = 6`.

Thus, the equation of this line would be
`y = -3\, x + 6`.