Post by Admin on Oct 3, 2016 20:03:45 GMT
Slope of a Line
Draw this up yourself as I go through it so you can follow it easily
Step 1
Remember this equation: Slope = the change in y divided by the change in x.
Step 2
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.
Step 3
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!
Step 4
The long way: Find two points on the line. First let x=0:
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, let y=0:
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 slope of a line formula with these two points: Change in y = 8 - 0 = 8. Change in x = -4 -0 = -4. 8/-4 = -2. Your slope is -2.
Step 5
The Easy way: Look at you 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. 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. Compare the equation y = mx + b and your re-arranged equation. Which number in that equation is m? -2. So there's no calculations, just a little bit of re-arranging and you have your slope =]
Draw this up yourself as I go through it so you can follow it easily
Step 1
Remember this equation: Slope = the change in y divided by the change in x.
Step 2
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.
Step 3
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!
Step 4
The long way: Find two points on the line. First let x=0:
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, let y=0:
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 slope of a line formula with these two points: Change in y = 8 - 0 = 8. Change in x = -4 -0 = -4. 8/-4 = -2. Your slope is -2.
Step 5
The Easy way: Look at you 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. 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. Compare the equation y = mx + b and your re-arranged equation. Which number in that equation is m? -2. So there's no calculations, just a little bit of re-arranging and you have your slope =]