Question

(a) Write down the gradient of the line with equation y = 7 - 4x The line L passes through the points with coordinates (- 3, 1) and (2, - 2)

Answer 1

Note: Let us consider, we need to find the gradient of line L.

Given:

The given equation of a line is:

`y=7-4x`

The line L passes through the points with coordinates (- 3, 1) and (2, - 2).

To find:

The gradient of the given line and the gradient of line L.

Solution:

Slope intercept form of a line is:

`y=mx+b` ...(i)

We have,

`y=7-4x` ...(ii)

On comparing (i) and (ii), we get

`m=-4`

Therefore, the gradient of the given line is -4.

The line L passes through the points with coordinates (- 3, 1) and (2, - 2). So, the gradient of line L is:

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

`m=(-2-1)/(2-(-3))`

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

`m=(-3)/(5)`

Therefore, the gradient of the line L is
`(-3)/(5)`.