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:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

$m=\dfrac{-2-1}{2-(-3)}$

$m=\dfrac{-3}{2+3}$

$m=\dfrac{-3}{5}$

Therefore, the gradient of the line L is $\dfrac{-3}{5}$.