Question

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

Answer 1

Answer:

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

Step-by-step 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:

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

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