Answer:
the equation that passes through this is y= -7x-22
Explanation:
You want to find the equation for a line that passes through the point (-4,6) and has a slope of -7.
First of all, remember what the equation of a line is:
y = mx+b
Where:
m is the slope, and
b is the y-intercept
To start, you know what m is; it's just the slope, which you said was -7. So you can right away fill in the equation for a line somewhat to read:
y=-7x+b.
Now, what about b, the y-intercept?
To find b, think about what your (x,y) point means:
(-4,6). When x of the line is -4, y of the line must be 6.
Because you said the line passes through this point, right?
Now, look at our line's equation so far: b is what we want, the -7 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specifically passes through the point (-4,6).
So, why not plug in for x the number -4 and for y the number 6? This will allow us to solve for b for the particular line that passes through the point you gave!.
(-4,6). y=mx+b or 6=-7 × -4+b, or solving for b: b=6-(-7)(-4). b=-22.