Question

Find the slope of the line through (-2,5) and (-4,-4) and write answer in the simplest form.

Answer 1

use the slope formula

m = (y2 - y1)/(x2 - x1)

Answer 2

in this case

(x1,y1) = (-2,5)
(x2,y2) = (-4,-4)

Answer 3

(-2,5),(-4,-4)

Substitute in the values of x and y into the equation to find the slope.
m=(-4-(5))/(-4-(-2))

Multiply -1 by each term inside the parentheses.
m=(-4-(5))/(-4+2)

Add 2 to -4 to get -2.
m=(-4-(5))/(-2)

Move the minus sign from the denominator to the front of the expression.
m=-((-4-(5))/(2))

Multiply -1 by each term inside the parentheses.
m=-((-4-5)/(2))

Subtract 5 from -4 to get -9.
m=-((-9)/(2))

Move the -1 to the front of the fraction.
m=-(-((9)/(2))

Multiply -1 by each term inside the parentheses.
m=-(-(9)/(2))

Multiply -1 by each term inside the parentheses.
m=(9)/(2)

Slope is 9/2

Hope this helps. :)

Answer 4

So you know it's a line, right so let's whip out our template.

y=mx+b

Since we know these two points (-2,5) and (-4,-4) are on the line, then we can just plug them in:

5=m(-2)+b
-4=m(-4)+b

Now you have two equations and two unknowns to solve for. Plug one into the other or subtract one equation from the other. It's pretty quick and straightforward. No memorizing formulas, just direct application of what you know.

Answer 5

From here you can actually notice that by subtracting the second equation from the first you get:

5-(-4)=m(-2)-m(-4)

since the b's will cancel out. A little rearrangement with algebra gives:

[5-(-4)]/[-2-(-4)]=m

which should match up with our whole rise/run formula, except now we've derived it by just doing algebra on the general equation of a line which fits our conditions.