Question

How do you find the slope given A(2, -4) and B(4, 7)?

Answer 1

Slope = `11/2`

Explanation:

The slope, gradient or steepness of a line is defined as:

The `"the vertical change"/"the horizontal change"` which is written as

`(Delta y)/(Delta x) = "change in y"/"change in x"`

If you have any two points on a line you can find the slope of the line between them by using the formula:

`m = (y_2-y_1)/(x_2-x_1)" "` Either point can be `(x_1, y_1)`

We have `A(2,-4) and B(4,7)`

`m = (7-(-4))/(4-2) = (7+4)/2 = 11/2`

The slope is left in this form. This slope represents a very steep line which has a vertical increase of 11 for a horizontal change of only 2.

The line with this slope through the given points is shown below:
graph{y = 11/2x -15 [-44.56, 115.54, -32.3, 47.7]}

Answer 2

`+11/2`

Explanation:

`color(blue)("Preamble")`

The slop (gradient) is the amount up or down for a given amount of along reading left to right on the x-axis.

If the slop is like going up a hill then it is positive. On the other hand if it is like going down a hill then it is negative.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Looking at the x's; the left most point is A as 2 is less than 4.
So we read from point A to point B

Let point 1 be `P_1->(x_1,y_1)=(2,-4)->A`
Let point 2 be `P_2->(x_2,y_2)=(4,7)->B`

The gradient `m->("change in y")/("change in x")->(y_2-y_1)/(x_2-x_1)`

Some people write this as `(Deltay)/(Deltax) = m` where

`Deltay` means change in `y` and `Deltax` means change in `x`

`color(brown)("So we have:")`

`"gradient "->m=(y_2-y_1)/(x_2-x_1)=(7-(-4))/(4-2)=+11/2`

As positive it means the 'slope' is upwards reading left to right.