Question

The equation of a line is 5x+2y=6 find the gradient and y-intercept this line

Answer 1

`the \: gradient(slope) = - \frac {5}{2}`

`the \: y - intercept = 3`

Explanation:

Greetings!!!

To find the gradient (slope intercept)

Firstly recall that y=mx+b

where, m= gradient (slope intercept)

Thus,

`5x + 2y = 6`

solve for y

`2y = - 5x + 6`

divide both sides of the expression by 2

`(2y)/(2) = ( - 5x + 6)/(2)`

solve for y

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

So, the gradient equals to

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

Secondly, to find y-intercept let x=0

`5(0) + 2y = 6`

solve for y.

`2y = 6`

divide both sides of the expression by 2.

`(2y)/(2) = (6)/(2)`

solve for y.

`y = 3`

Finally, the y - intercept equals to 3

If you have any questions tag it on comments

Hope it helps!!!

Answer 2

Explanation:

Arrange the given equation into y = mx + b form

then m = gradient b = intercept

5x + 2y = 6

2y = - 5x + 6

y = -5/2 x + 3 gradient = - 5/2 intercept = 3