Question

Write an equation in point-slope form of the line that passes through the point 4,-1and has slope of -5

Answer 1

Answer:

y=-5+19

Step-by-step explanation:

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 -5. So you can right away fill in the equation for a line somewhat to read:

y=-5x+b.

Now, what about b, the y-intercept?

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

(4,-1). When x of the line is 4, y of the line must be -1.

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 -5 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,-1).

So, why not plug in for x the number 4 and for y the number -1? This will allow us to solve for b for the particular line that passes through the point you gave!.

(4,-1). y=mx+b or -1=-5 × 4+b, or solving for b: b=-1-(-5)(4). b=19.