Question

The equation of line L is 3x − 4y = 24. The line intersects the X − axis at A and the

Y − axis at B. Given that M is the point (4, −3) and O is the origion. Find

. The gradient of line L.

Answer 1

The slope of the line = m = 3/4

Explanation:

We know that the slope-intercept of line equation is

`y=mx+b`

Here:

• m is the slope

• b is the y-intercept

Given the equation of line L

`3x - 4y = 24`

Writing the equation in the slope-intercept form

`3x - 4y = 24`

Add -3x to both sides

`3x\:-\:4y+\left(-3x\right)=\:24+\left(-3x\right)`

`-4y=\:-3x+24`

Divide both sides by -4

`-(4y)/(4)=\:(\left-3x+24\right)/(-4)`

`y=(3)/(4)x-6`

Comparing the equation with
`y=mx+b`

Therefore, the slope of the line = m = 3/4