Answer:
y+4=-6(x+8) point-slope form
y=-6x-52 slope-intercept form
6x+y=-52 standard form
Explanation:
Slope-intercept form of a line is y=mx+b where m is the slope and b is the y-intercept.
Lines that are perpendicular have opposite reciprocal slopes.
So the slope of y=(1/6)x+3 is 1/6.
The opposite reciprocal of (1/6) is -6.
So the equation for the line we are looking for is in the form:
y=-6x+b (Since the slope of our new line is -6)
Now we want our line to go through (-8,-4).
So plug that in:
-4=-6(-8)+b
-4=48+b
Subtract 48 on both sides:
-52=b
The equation for the line we are looking for is
y=-6x-52.
Now you could do other forms.
Another one is point-slope form.
We already know it goes through (-8,-4) and a slope of -6.
Point slope form is: y-y1=m(x-x1) where m is the slope and (x1,y1) is a point on the line.
Plug in the information to get:
y-(-4)=-6(x-(-8))
y+4=-6(x+8)
I'm going to do one more form.
Standard form is ax+by=c where a,b,c are integers.
y=-6x-52
Add 6x on both sides:
6x+y=-52