Question

What is the equation of the line that passes through the point (4,−2) and has a slope of −2?​

Answer 1

Answer:y=-2x+6

Step-by-step explanation:

You want to find the equation for a line that passes through the point (4,-2) and has a slope of -2.

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 -2. So you can right away fill in the equation for a line somewhat to read:

y=-2x+b.

Now, what about b, the y-intercept?

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

(4,-2). When x of the line is 4, y of the line must be -2.

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 -2 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,-2).

So, why not plug in for x the number 4 and for y the number -2? This will allow us to solve for b for the particular line that passes through the point you gave!.

(4,-2). y=mx+b or -2=-2 × 4+b, or solving for b: b=-2-(-2)(4). b=6.