Question

How do you find the slope and intercept of `3x+7=0`?

Answer 1

The slope is 3 and the intercept is 7.

Explanation:

First off the equation should read `3x + 7 = y` just easier to make sense of.

The values you are looking for are in the formula:

The slope is a ratio of how much `y` increases based on how much `x` increases, it's usually calculated based on the "rise over run" it looks like this:

`"rise (increase in y)"/"run (increase in x)"`

In the case of this formula, `y` increases 3 units for every unit `x` increase. I'll put a graph in and you can pick any 2 points on the line and find the amount `x` and `y` increases (say `y=0;x=5` and `y=15;x=10` then in amount y increases is 15 units while x increases by 5) then the slope is calculated like this:

`15/5=3` This gives you the 3 in the equation `color(red)(3)x+7=y`

The intercept is the value of `y` when `x` equals 0. If you substitute `x=0` into the equation you can see that the only thing left to that gives a value is 7.

`cancel(3(0))+7=y -> y=7` When `x=0` So 7 is your intercept.

graph{3x+7 [-12.3, 16.17, -2.06, 12.18]}

Answer 2

`"see explanation"`

Explanation:

`"subtract 7 from both sides and divide by 3 gives"`

`x=-7/3`

`"this is the equation of a vertical line parallel to the y-axis"`
`"passing through all points with an x-coordinate of "-7/3`

`"the slope is therefore undefined"`

`"the x-intercept "=-7/3" there is no y-intercept"`
graph{(y-1000x-2333)=0 [-10, 10, -5, 5]}