Question

What is an equation of the line that passes through the point (-4, -6) and is

Answer 1

Answer:y=2/3x-10/3
- 4/-6 is 4/6 so m is 4/6 then fill in the x and y variables in y=Mx+b solve for b then start plotting the equation of the line to check and you get your answer

I think this is the answer you might need to check again with more people

Answer 2

Answer:

The required equation is: $\mathbf{x+2y=-16}$

Step-by-step explanation:

We need to find equation of the line that passes through the point (-4, -6) and is  perpendicular to the line

The equation of line will be in the slope intercept form $y=mx+b$

where m is slope and b is y-intercept.

Finding Slope

First transforming the given equation $2x -y = 6$ in slope-intercept form:

$2x -y = 6\\-y=-2x+6\\y=2x-6$

Now comparing the equation with general equation of slope intercept form We get slope m= 2

Since the two lines are perpendicular, the slope of new line will be opposite reciprocal of given line i.e $m=-\frac{1}{m}$

So, Slope of required line is: $m=-\frac{1}{2}$

Finding y-intercept

y-intercept can be found using slope $m=-\frac{1}{2}$ and point (-4,-6) as follows

$y=mx+b\\-6=-\frac{1}{2}(-4)+b\\-6=+2+b\\b=-6-2\\b=-8$

So, y-intercept b = -8

Finding equation of line:

The equation of line having slope $m=-\frac{1}{2}$ and y-intercept b = -8 is:

$y=mx+b\\y=-\frac{1}{2}(x)-8$

Now, writing the equation in standard form i.e Ax+By=C

$y=-\frac{1}{2}(x)-8 \\ Multiply \ by \ 2\\2y=-x-16\\x+2y=-16$

So, the required equation is: $\mathbf{x+2y=-16}$