Question

How do you graph using the intercepts for `2x+6y=0`?

Answer 1

Refer to explanation below.

Explanation:

`2x + 6y = 0`

First rearrange the equation.
`2x + 6y = 0`
`6y = 0 - 2x`
`y =` `(-2x)/6`

Now, substitute x = 0 into the equation to find the intersection with the y-axis.
`y=(-(2*0))/6`
`y=0/6`
`y=0`
Therefore the graph intersects the y-axis at (0, 0)

Now, substitute y = 0 into the equation to find the intersection with the x-axis.
`0=(-(2x))/6`
`6*0=-2x`
`0/-2=x`
Therefore the graph intersects the x-axis at (0, 0)

The gradient of the graph is found by looking at the coefficient of x.
`y=(-(2x))/6`
`y=(-(1x))/3`
`y=(-1/3)x`
Therefore the graph is observed to have a negative gradient with the value of `1/3`

graph{2x + 6y = 0 [-10, 10, -5, 5]}