Question

Find the gradient for the line 12x+4y=8

Answer 1

gradient = - 3

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the gradient and c the y- intercept )

given

12x + 4y = 8 ( subtract 12x from both sides )

4y = - 12x + 8 ( divide through by 4 )

y = - 3x + 2 ← in slope- intercept form

with gradient m = - 3

Answer 2

-3

Explanation:

To find the gradient of the line
`\sf 12x+4y=8`, we can rearrange the equation into slope-intercept form, y = mx + b, where m is the gradient of the line and b is the y-intercept.

`\sf 12x+4y=8`

To do this, we can subtract 12x from both sides of the equation to get:

`\sf 12x+4y-12x =-12x + 8`

`\sf 4y = -12x+8`

Then, we can divide both sides by 4 to get:

`\sf (4y)/(4) =( -12x+8)/(4)`

`\sf y = -3x+2`

While comparing with y = mx + b, we get

m = -3

Therefore, the gradient of the line is -3.