What is the slope of the line going through (5, -4) and (6, -2)?

2 Answers
Dec 5, 2017

See a solution process below:

Explanation:

The slope can be found by using the formula: m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))m=y2y1x2x1

Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) are the two points on the line.

Substituting the values from the points in the problem gives:

m = (color(red)(-2) - color(blue)(-4))/(color(red)(6) - color(blue)(5)) = (color(red)(-2) + color(blue)(4))/(color(red)(6) - color(blue)(5)) = 2/1 = 2m=2465=2+465=21=2

Use the slope equation
The slope is m=2m=2.

Explanation:

m = ("change in " y)/("change in " x)m=change in ychange in x

The letter mm is used to represent the slope.

Call one point (x_1,y_1)(x1,y1) and the other point (x_2,y_2)(x2,y2)

Then

m = (y_2-y_1)/(x_2-x_1)m=y2y1x2x1

So if (5,-4)(5,4) is (x_1,y_1)(x1,y1) and (6,-2)(6,2) is (x_2,y_2)(x2,y2), then The slope equation states

m = (y_2-y_1)/(x_2-x_1) = (-2-(-4))/(6-5) = 2/1= 2m=y2y1x2x1=2(4)65=21=2

The slope equals two.