Question

Find the slope and the x- & y-intercepts of x + 2y = 6(5 pts) (Show work for finding X- & y-intercepts)

Answer 1

First, we need to write our equation in standard form — the y should be on the left- hand - side and the x should be on the right- hand side.

The first step is to subtract x from both sides, doing this we get:

`2y=6-x`

Now we divide both sides of the equation by 2 (this isolates the y on LHS), doing this gives us:

`y\text{ = }(6-x)/(2)`

which can also be written as

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

The y-intercept is the point at which the line described by our equation intersects the y-axis. This intersection happens when x = 0; therefore, the y-intercept is

`y=(-0)/(2)+\text{ 3}`
`y=0\text{.}`

The x-intercept is the point at which the line intersects the x-axis. This happens when y =0; therefore, the x-intercept is

`0=(-x)/(2)+3`
`-3\text{ = }(-x)/(2)`
`x\text{ = 6.}`

Now we see that the slope of the equation is -1/2 (the coefficient of x ). The y-intercept is y = 3 and the x-intercept is 6.