Question

The equation of line L is 3x - 8y + 20 = 0.
Find the gradient of line L.

Answer 1

The slope or gradient of the line L will be: m = 3/8

Explanation

We know that the slope-intercept form of the line equation

`y = mx+b`

where m is the slope or gradient and b is the y-intercept

Given the equation of the line

`3x - 8y + 20 = 0`

Let us solve for 'y' to write the equation in the slope-intercept form

`3x - 8y + 20 = 0`

Add -3x to both sides

`3x-8y+20+\left(-3x\right)=0+\left(-3x\right)`

simplify

`-8y+20=-3x`

subtract 20 from both sides

`-8y+20-20=-3x-20`

simplify

`-8y=-3x-20`

Divide both sides by -8.

`(-8y)/(-8)=(-3x-20)/(-8)`

`y=(3)/(8)x+(5)/(2)`

Thus, comparing with the slope-intercept form

`y = mx+b`

`m\:=\:(3)/(8)`

Thus, the slope or gradient of the line L will be: m = 3/8