Question

Find the equation of the line with slope m=−2 that contains the point (−7,16).

Answer 1

`y = -2\, x + 2`.

Explanation:

If a line of slope
`m` goes through the point
`(x_(0),\, y_(0))`, the equation of this line in point-slope form would be:

`y - y_(0) = m\, (x - x_(0))`.

For example, the slope of the line in this question is
`(-2)`, thus
`m = -2`; The line goes through the point
`(-7,\, 16)`, thus
`x_(0) = -7` whereas
`y_(0) = 16`.

Substitute in these values to find the equation of this line in the point-slope form:

`y - 16 = (-2)\, (x - (-7))`.

Simplify and rewrite to find the equation of this line in the slope-intercept form:

`y - 16 = -2\, (x + 7)`.

`y = -2\, x + 2`.