Question

The gradient of the line segment between the points (2,-3) and (4,-7).

Answer 1

To find the gradient of a line you use this equation: Rise / Run

I am assuming this is a graph where both the x and y-axis increase in value by one.

So first of all, you should draw out this graph.

Second, draw a point at each of the given coordinates.

Now, join these points by drawing a right angle triangle. Put simply, draw a line from the point (4, -7) down until it is on the same level as the point (2, -3), then draw a line across.

Finally, measure the length of both these sides and use them in the equation above.

Let's assume the rise (vertical line) and the run (horizontal line) are 5 and 8 respectively. We can do 5/8 to get a gradient which is 0.625.

Answer 2

gradient = - 2

Explanation:

Calculate the gradient (slope ) m using the gradient formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (2, - 3 ) and (x₂, y₂ ) = (4, - 7 )

m =
`(-7-(-3))/(4-2)` =
`(-7+3)/(2)` =
`(-4)/(2)` = - 2