What is an equation of the line that passes through the point (-4, -6) and is perpendicular to the line 2x -y = 6?

The required equation is:

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

where m is slope and b is y-intercept.

Finding Slope

First transforming the given equation in slope-intercept form:

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

So, Slope of required line is:

Finding y-intercept

y-intercept can be found using slope and point (-4,-6) as follows

So, y-intercept b = -8

Finding equation of line:

The equation of line having slope and y-intercept b = -8 is:

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

So, the required equation is:

y=-2.5x+12.5

step-by-step explanation:

5y=2x+10

y=0.4x+2

slope=-2.5

5=-2.5*3+b

b=12.5