Question

Write an equation in point-slope form of the line through point P(-4, 7) with slope -4.

Answer 1

y - 7 = -4(x + 4)

Explanation:

The point-slope equation is y - k = m(x - h), where (h, k) is the given point and m is the slope of the line.

We substitute -4 for h, 7 for k and -4 for m, obtaining:

y - 7 = -4(x + 4)

Answer 2

y - 7 = -4(x + 4)

Explanation:

You want to find the equation for a line that passes through the point (-4,7) and has a slope of -4.

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 -4. So you can right away fill in the equation for a line somewhat to read:

y=-4x+b.

Now, what about b, the y-intercept?

To find b, think about what your (x,y) point means:

(-4,7). When x of the line is -4, y of the line must be 7.

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 -4 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 specfically passes through the the point (-4,7).

So, why not plug in for x the number -4 and for y the number 7? This will allow us to solve for b for the particular line that passes through the point you gave!.

(-4,7). y=mx+b or 7=-4 × -4+b, or solving for b: b=7-(-4)(-4). b=-9.