When looking at the slope in an algebraic perspective, you begin with two points on a line: (x1,y1) and (x2,y2).
Since we know that the slope is a rate of change, we can think of it as the "change in y" over (or divided by) "the change in x".
m= change in y / change in x
But what does "change" mean here? How much "y" or "x" changes simply means how far you've travleled on the graph so algebraically speaking you subtract.
m = y2-y1 / x2 - x1
Now that we understand the formula, let's plug in some numbers and see if we can apply it.
Find the slope of the line containing the following two points: (1,2) and (3,5).
step 1: label the values (x1=1,y1=2) and (x2=3, y2=5)
step 2: plug the values into the formula: m = y2-y1 / x2-x1
m = 5-2 / 3-1
so m = 3/2
Now practice on your own and click on the link below to check your answers.
1. Find the slope of the line containing the following two points: (5,12) and (6,17).
2. Find the slope of the line containing the following two points: (4,9) and (8,13).
3. Find the slope of the line containing the following two points: (7,3) and (5,6)
Hmmm.....? Can slopes have negative values? Let's work this one out and see.
step 1: label the values (x1=7,y1=3) and (x2=5, y2=6)
step 2: plug the values into the formula: m = y2-y1 / x2-x1
m = 6-3 / 5-7
so m = 3/-2
Yes, the slope can be negative. That simply means that the line is pointing in the other direction or you are going in debt instead of gaining so many dollars per hour.
Now continuing practicing (click the link below to check your answers):
4. Find the slope of the line containing the following two points: (7,4) and (3,1).
5. Find the slope of the line containing the following two points: (3,5) and (2,11).
6. Find the slope of the line containing the following two points: (2,13) and (5,4)
When looking at the slope in an algebraic perspective, you begin with two points on a line: (x1,y1) and (x2,y2).
Since we know that the slope is a rate of change, we can think of it as the "change in y" over (or divided by) "the change in x".
m= change in y / change in x
But what does "change" mean here? How much "y" or "x" changes simply means how far you've travleled on the graph so algebraically speaking you subtract.
m = y2-y1 / x2 - x1
Now that we understand the formula, let's plug in some numbers and see if we can apply it.
Find the slope of the line containing the following two points: (1,2) and (3,5).
step 1: label the values (x1=1,y1=2) and (x2=3, y2=5)
step 2: plug the values into the formula: m = y2-y1 / x2-x1
m = 5-2 / 3-1
so m = 3/2
Now practice on your own and click on the link below to check your answers.
1. Find the slope of the line containing the following two points: (5,12) and (6,17).
2. Find the slope of the line containing the following two points: (4,9) and (8,13).
3. Find the slope of the line containing the following two points: (7,3) and (5,6)
Hmmm.....? Can slopes have negative values? Let's work this one out and see.
step 1: label the values (x1=7,y1=3) and (x2=5, y2=6)
step 2: plug the values into the formula: m = y2-y1 / x2-x1
m = 6-3 / 5-7
so m = 3/-2
Yes, the slope can be negative. That simply means that the line is pointing in the other direction or you are going in debt instead of gaining so many dollars per hour.
Now continuing practicing (click the link below to check your answers):
4. Find the slope of the line containing the following two points: (7,4) and (3,1).
5. Find the slope of the line containing the following two points: (3,5) and (2,11).
6. Find the slope of the line containing the following two points: (2,13) and (5,4)