You can put this solution on YOUR website! A straight line has a "slope" and an "intercept".
In simple terms, the slope is how steeply angled the line is when you draw it as a graph (with y up the vertical axis and x along the horixontal axis). The "intercept" is where the line crosses the y axis. You don't need to worry about this since it's not in the question, but it's easy to find out.
If you can re-work your equation into the form :
y = ax + b (where a and b are numbers)
.. then the slope of the line is the number "a" and the intercept is the number "b".
[Note : in some textbooks (and maybe also by your maths teacher), the formula is written using the letters "m" and "c", so it looks like this :
y = mx + c (where m and c are numbers). It's the same thing, just using different letters for the constants]
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Now : onto your question.
-4x + 2y = 11
We're gonna need to play around with it to get it looking like y = ax + b
Let's start out by adding 4x onto both sides of the equation :
2y = 11 + 4x
Since it doesn't matter which way round you do an addition sum, we can neaten that up a bit by swopping the two terms around on the right hand side :
2y = 4x + 11
Nearly there ! Now, halve both sides :
y = 2x + 5.5
So the slope of the graph is 2 (ANSWER)
Here is how the graph looks if you draw it in a typical cartesian form :
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