Respuesta :
ANSWER:
The equation of the line passing through the point (8,-6) and parallel to line with slope -2 is 2x + y -10 = 0.
SOLUTION:
Given, a line is passing through the point (8, −6) and is parallel to another line, whose slope is −2
We need to find the equation of the line.
We know that, parallel lines will have same slope.
So slope of the required line is -2.
Now, we have a point on the line and slope of the line, so we can use point – slope form to find the line equation.
Point slope form is given as
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
Where "m" is the slope and [tex]\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)[/tex] is a point on that line.
Here, [tex]\mathrm{m}=-2, \mathrm{x}_{1}=8 \text { and } \mathrm{y}_{1}=-6[/tex]
Now, substitute values in point slope form.
y – (-6) = -2(x – 8)
y + 6 = -2x - 2(-8)
y + 6 = -2x + 16
2x + y +6 -16 = 0
2x + y -10 = 0
Hence, the equation of the line is 2x + y -10 = 0.
