Find the slope of a linear function :
To find the slope from a graph first we have to mark any two points on the graph.
After marking two points we have to draw the right triangle which connects the points which have been marked. In the right triangle,
Rise |
Run | |
If the direction is towards upward, we have to take "positive" sign. If the direction is towards downward, we have to take "Negative" sign. |
If the direction is towards the right side, we have to take "positive" sign. If the direction is towards the left side, we have to take "Negative" sign |
Alternate method :
We can use the formula (y₂-y₁)/(x₂-x₁) to find the slope of the line. Here (x₁, y₁) and (x₂, y₂) are any points lie on the line.
Example 1 :
Find the slope from the graph find the slope from a graph
Solution :
Now we are going to mark two points (-2, 0) and (0, 4) on the line to find the slope.
Slope = Change of y/change of x
"We have to rise before we run"
We need to take downward direction from (0,4) for rise.Since we take downward direction we have to put negative sign.
Rise = -4
After reaching the common point we need to move towards to the left ward 2 units. So we have to take -2.
Run = -2
= (- 4) / (-2) = 2
Hence, slope of the given line is 2.
By using the alternative method, we will get the same answer.
m = (y₂-y₁)/(x₂-x₁)
(x₁,y₁) ==> (-2, 0) and (x₂, y₂) ==> (0, 4)
m = (4 - 0)/(0 + 2)
m = 4 /2 = 2
Let us see the next example of the topic "Find the slope of a linear function".
Example 2 :
Find the slope from the graph
Solution :
Now we are going to mark two points (1, -1) and (2, 1) on the line to find the slope.
Slope = Change of y/change of x
"We have to rise before we run"
We need to take downward direction from (2,1) for rise.Since we take downward direction we have to put negative sign.
Rise = -2
After reaching the common point we need to move towards to the left ward 1 unit. So we have to take -1.
Run = -1
= (-2) / (-1) = 2
Hence, slope of the given line is 2.
By using the alternative method, we will get the same answer.
m = (y₂-y₁)/(x₂-x₁)
(x₁,y₁) ==> (1, -1) and (x₂, y₂) ==> (2, 1)
m = (1 + 1)/(2 - 1)
m = 2 / 1 = 2
Let us see the next example of the topic "Find the slope of a linear function".
Example 3 :
Find the slope from the graph
Solution :
Now we are going to mark two points (-2, -2) and (-1, 3) on the line to find the slope.
Slope = Change of y/change of x
"We have to rise before we run"
We need to take upward direction from (-2, -2) for rise.Since we take upward direction we have to put positive sign.
Rise = 5
After reaching the common point we need to move towards to the right side 1 unit. So we have to take 1.
Run = 1
= 5 / 1 = 5
Hence, slope of the given line is 5.
By using the alternative method, we will get the same answer.
m = (y₂-y₁)/(x₂-x₁)
(x₁,y₁) ==> (-2, -2) and (x₂, y₂) ==> (-1, 3)
m = (3 + 2)/(-1 + 2)
m = 5 / 1 = 5
Example 4 :
Find the slope from the graph
Solution :
Now we are going to mark two points (1, 4) and (0, -3) on the line to find the slope.
Slope = Change of y/change of x
"We have to rise before we run"
We need to take downward direction from (1, 4) for rise.Since we take downward direction we have to put negative sign.
Rise = -7
From the common point we need to move towards to the left side 1 unit to reach (0, -3). So we have to take -1.
Run = -1
= -7 / (-1) = 7
Hence, slope of the given line is 7.
By using the alternative method, we will get the same answer.
m = (y₂-y₁)/(x₂-x₁)
(x₁,y₁) ==> (1, 4) and (x₂, y₂) ==> (0, -3)
m = (-3 - 4)/(0 - 1)
m = (-7) / (-1) = 7
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