Question

What is the slope of the line passing through the following points: `(-3, 8), (1,6)`?

Answer 1

`m = -1/2`

Explanation:

To find the gradient (slope) of a line passing through 2 points

use the `color(blue)" gradient formula "`

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

where`(x_1 , y_1 ) " and " (x_2 , y_2 ) " are the coords of 2 points"`

here let`(x_1,y_1) = (-3,8) " and " (x_2,y_2) = (1,6)`

`rArr m = (6-8)/(1-(-3)) = (-2)/4 = -1/2`

Answer 2

`color(blue)("The gradient of "-1/2" is negative meaning that the")` `color(blue)(" values are reducing")`

Explanation:

Slope (gradient) is the amount of up or down for a given amount of along. Think of the slope of a hill!

So the gradient is

`color(blue)(("change in up/down")/("change in along")" "->" "("change in the y-axis")/("change in the x-axis"))`

You list (-3,8) first so we will take that as the starting point `(x_1,y_1)`

Let `(x_1,y_1)" "->" "(-3,8)`
Let `(x_2,y_2)" "->" "(1,6)`

`" "("change in the y-axis")/("change in the x-axis")" "->" "(y_2-y_1)/(x_2-x_1)`

For your question this gives:

`" "(6-8)/(1 -(-3))" "=" "(-2)/4" "=" "-2/4" "=" "-1/2`

The negative gradient means that the graph 'goes down' as you move from left to right

`color(blue)("The gradient of "-1/2" is negative meaning that the")` `color(blue)("values are reducing")`