Find the gradient and y-intercept in this equation: 8x+2y+9=0

Question

Find the gradient and y-intercept in this equation:

`8x+2y+9=0`

Answer 1

Gradient: -4

y-intercept:
`-(9)/(2)`

Explanation:

Step 1 - Subtract 8x from both sides to isolate the 2y + 9

`8x + 2y + 9 = 0\\8x + 2y + 9 - 8x = 0 - 8x\\2y + 9 = -8x\\`

Step 2 - Subtract 9 from both sides to isolate the 2y:

`2y + 9 = -8x\\2y + 9 - 9 = -8x - 9\\2y = -8x - 9`

Step 3 - Divide both sides of the equation by 2:

`(2y)/(2) = (-8x)/(2) - (9)/(2)\\y = -4x - (9)/(2)`

In this form, y = mx + b, the m value is the gradient with the b value being the y-intercept. This means:

`y = -4x - (9)/(2)\\\\m = -4\\b = -(9)/(2) \\\\`

Resulting in the gradient being -4 and the y-intercept being
`-(9)/(2)`.

Hope this helps!