Question

Write an equation of a line which is passing through the point (8, −6) and is parallel to another line, whose slope is −2

Answer 1

-6=-2(8)+b
-6=-16+b
10=b
Equation: y=-2x+b

Answer 2

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

`y-y_(1)=m\left(x-x_(1)\right)`

Where "m" is the slope and
`\left(\mathrm{x}_(1), \mathrm{y}_(1)\right)` is a point on that line.

Here,
`\mathrm{m}=-2, \mathrm{x}_(1)=8 \text { and } \mathrm{y}_(1)=-6`

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.