Question

Find the slope of AB

Answer 1

Given question:

• find the slope of AB

What do we know about AB? We're only given two points (the endpoints) of the segment AB. These points are (4,1) and (-1,3). With this pair of points, we can utilize the slope formula

`\rightleftharpoons m=\cfrac{y_2-y_1}{x_2-x_1}`

Instead of the y's and x's, we substitute the endpoints of AB:

`\rightleftharpoons m=\cfrac{3-1}{-1-(-4)}`

`\rightleftharpoons m=\cfrac{2}{-1+4}}`

`\rightleftharpoons m=-\cfrac{2}{3}`

∴ slope of AB = negative two-thirds

Answer 2

`(2)/(3)`

Explanation:

Slope describes the steepness and direction of a line.

Defining Slope

The slope is the rise over run of a line. This means that slope describes the change in y divided by the change in x. The slope can tell us the steepness and direction of a line. The larger the slope, the steeper the line will be. Additionally, if the slope is positive then the line will increase to the right.

Slope Formula

One way to find the slope of a line is by using the slope formula. The formula is:

• 
  `\displaystyle (y_(2)- y_(1) )/(x_(2) -x_(1) )`

So, we can plug in the coordinate points of A and B into this formula. For the sake of this question, we can use B as point 2.

• 
  `(3 - 1)/(-1-(-4))=(2)/(3)`

So, the slope of AB is 2/3.