Question

What is the slope of a line that with the points (2,4) and (4,-2)?

Answer 1

`color(brown)(-3)`
`color(white)(..)`
`color(blue)("Detailed explanation given about how it all works!")`

Explanation:

`color(blue)("Assumption:")`

The line is for a strait line graph

`color(blue)("Pre amble.")`

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

The state of up or down is determined as you move from left to right. Like the positive way of counting on the number line.

The degree of up/down change is measured on the y-axis (vertical number line). The degree of along is measured on the x-axis (horizontal number line).

The slope is defined as negative if it is going down (left to right) and positive if it is going up (left to right). This because of the way the numbers work.

`color(blue)("Solving your question")`

Slope (gradient) =`("change in y-axis")/("change in x-axis")`

So if we use rhs for right hand side and lhs for left hand side then we have:

Slope (gradient) =`("change in y-axis")/("change in x-axis") =(y_("rhs") -y_("lhs"))/(x_("rhs")-x_("lhs"))`

`color(brown)("Assuming that "(2,4)-> lhs " and "color(blue)( (4,-2)->rhs))`

Slope (gradient)=`color(brown)((color(blue)((-2))-4)/(color(blue)(4)-2)) = (-6)/2 = -3/1 =-3`

So for every 1 along the graph line goes `color(green)("down 3 ")`because of this the `color(green)("gradient is negative 3")`