Question

For the linear equation `y=2x+4`, if `x` increases by 1 point, how much will `y` increase?

Answer 1

`Y` will increase by `2`.

Explanation:

graph{y=2x+4 [-8.71, 16.6, 0.49, 13.13]}

The graph above is the graph to the equation `y=2x+4`.

To solve this, I grabbed a random coordinate from the graph. The coordinates were `(1,6)`. I plugged them into the equation.

`6=2(1)+4`

Great! We know the equation works fine. But the question is what will happen to `y` if `x` increased by `1`. So what did I do? I increased `x` by `1` and kept the `y` as a variable so I could solve for it:

`y=2(2)+4`

`y=4+4`

`y=8`

Now let's check our work. Find the `2` on the x-axis and go up until the line runs in the corner of a square. And where could that be? On the number `8` on the y-axis! When `x` was `1`, `y` was `6`. When `x` was 2, `y` was `8`!

When `x` increased by `1`, `y` increased by `2`!