Question

How do you find the x and y intercepts and slope if they exist and graph the line -2x + 7y = 14?

Answer 1

The x intercept is where `y=0` or `-2x=14` so is `x=-7.`

For the slope and y intercept we write `7y=2x+14` or `y=2/7 x + 2` and read off the slope of `2/7` and y intercept at `y=2.`

Answer 2

`y` intercept: `(0,2)`

`x` intercept: `(-7,0)`

Slope: `2/7`

Explanation:

To find the intercepts, set one of the coordinates to zero and solve for the other:

`y` intercept: (set `x=0`)

`-2x + 7y = 14 \to 7y=14 \to y=2`

So, the `y` intercept is `(0,2)`

`x` intercept: (set `x=0`)

`-2x + 7y = 14 \to -2x=14 \to x=-7`

So, the `x` intercept is `(-7,0)`

To find the slope, it is convenient to write the equation in the form

`y = mx+q`

once this is done, the slope will be `m`. To reach or goal, let's add `2x` to both sides to get

`-2x + 7y = 14 \to 7y=2x+14`

and finally divide both sides by `7` to get

`y = 2/7 x + 2`

So, the slope is `2/7`