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

2 Answers
Jim G.
Feb 27, 2016

m = -1/2m=−12

Explanation:

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

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

m = (y_2 - y_1 )/(x_2 - x_1 ) m=y2−y1x2−x1

where (x_1 , y_1 ) " and " (x_2 , y_2 ) " are the coords of 2 points"(x1,y1) and (x2,y2) are the coords of 2 points

here let(x_1,y_1) = (-3,8) " and " (x_2,y_2) = (1,6) (x1,y1)=(−3,8) and (x2,y2)=(1,6)

rArr m = (6-8)/(1-(-3)) = (-2)/4 = -1/2 ⇒m=6−81−(−3)=−24=−12

Tony B
Feb 27, 2016

color(blue)("The gradient of "-1/2" is negative meaning that the")The gradient of −12 is negative meaning that thecolor(blue)(" values are reducing") 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"))change in up/downchange in along → change in the y-axischange in the x-axis

You list (-3,8) first so we will take that as the starting point (x_1,y_1)(x1,y1)

Let (x_1,y_1)" "->" "(-3,8)(x1,y1) → (−3,8)
Let (x_2,y_2)" "->" "(1,6)(x2,y2) → (1,6)

" "("change in the y-axis")/("change in the x-axis")" "->" "(y_2-y_1)/(x_2-x_1) change in the y-axischange in the x-axis → y2−y1x2−x1

For your question this gives:

" "(6-8)/(1 -(-3))" "=" "(-2)/4" "=" "-2/4" "=" "-1/2 6−81−(−3) = −24 = −24 = −12

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")The gradient of −12 is negative meaning that thecolor(blue)("values are reducing")values are reducing

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