A line has a slope of -6 that passes through the point (-12,5).
What is the equation of the line?
a. 6x + y = -77 <-- or C?
b. 6x + y = -67
c.-6x + y = 77
d.-6x + y = 17
To find the equation of a line given its slope and a point that the line passes through, you can use the point-slope form of a linear equation. The point-slope form is:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) is the given point.
In this case, the slope is -6, and the point the line passes through is (-12, 5). Plugging these values into the point-slope form, we get:
y - 5 = -6(x - (-12))
Simplifying, we get:
y - 5 = -6(x + 12)
Now we can expand the brackets:
y - 5 = -6x - 72
Finally, we can rewrite the equation in standard form, which is in the form Ax + By = C:
6x + y = -77
So the answer is a. 6x + y = -77.
Of the two choices, only a) and b) have a slope of -6
(-12,5) does not satisfy a) but it does satisfy b)
so b)
you just need to remember your point-slope form of a line, and you get
y-5 = -6(x+12)
Then just rearrange as needed.