First, remember this equation: Slope = the change in y divided by the change in x.
Let's use that equation to find the slope of a line with two points: (5,7) and (10, 22). The change in y is 22 - 7 = 15. The change in x is 10 -5 = 5. 15/5 = 3. See, that was easy!
But what happens if you don't have two points, just an equation?
4x-2y+16=0. You can find the slope two ways. The long way and the easy way!
The long way: Find two points on the line. First plug in zero for x:
4(0)- 2y + 16 = 0. Solve for y. 0 - 2y + 16 = 0; -2y = -16; y = 8.
Now you have one point on your line: (0,8).
Next, plug in 0 for y:
4x - 2(0) + 16 = o. Solve for x: 4x + 16 = 0; 4x = -16; x = -4.
Now you have the second point on your line: (-4, 0).
Now use your line slope formula with these two points: Change in y = 8 - 0 = 8. Change in x = -4 -0 = -4. 8/-4 = -2. Your slope is -2.
Seems like a lot of work, right? That's because it is. There's a faster way! Let's look at that equation again.
4x - 2y + 16 = 0.
If we can change it to the line format, we can easily see the slope. Change the equation to the format y = mx + b. It's easy - all you need to do is get y by itself on one side of the equation:
-2y + 16 = -4x; -2y = -4x - 16; y = -2x + 8.
The slope of the line is m. Which number in that equation is m? -2. That's right, just by looking at the equation, we can know the slope - without going through all the work we did the first time around! So much faster and easier!