Gradient of a Line 1
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Question 1 of 9
1. Question
Find the gradient of the line between the points A(1,4) and B(3,2)- m= (-1)
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The gradient (m) refers to the “gradient” or “slant” of a lineMethod OneGradient Formula
m=riserunTo find the gradient (m), measure the rise and run between two points on the lineFrom point (3,2) to (1,4) the rise is 2 units and the run is −2 unitsThe run is negative as the run goes to the leftm = riserun = 2−2 m = −1 m=−1Method TwoGradient Formula
m=y2−y1x2−x1First, choose any two coordinates on the line to use in the gradient FormulaWe have chosen the points: (1,4) and (3,2)Label the coordinates we chose from above(1,4)=(x1,y1)(3,2)=(x2,y2)Solve for the gradient (m) by substituting the two coordinates into the formulam = y2−y1x2−x1 Gradient Formula = 2−43−1 Plug in the coordinates = −22 Evaluate m = −1 −2÷2=−1 m=−1 -
Question 2 of 9
2. Question
Find the gradient of the line shown below- m= (3/2, 1.5)
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The gradient (m) refers to the “Gradient” or “slant” of a lineMethod OneGradient Formula
m=riserunTo find the gradient (m), measure the rise and run between two points on the lineFrom point (2,2) to (4,5) the rise is 3 units and the run is 2 unitsm = riserun = 32 m = 32 m=32Method TwoGradient Formula
m=y2−y1x2−x1First, choose any two coordinates on the line to use in the Gradient FormulaWe have chosen the points: (2,2) and (4,5)Label the coordinates we chose from above(2,2)=(x1,y1)(4,5)=(x2,y2)Solve for the gradient (m) by substituting the two coordinates into the formulam = y2−y1x2−x1 Gradient Formula = 5−24−2 Plug in the coordinates = 32 Evaluate m=32 -
Question 3 of 9
3. Question
Find the gradient of the line shown below- m= (2)
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The gradient (m) refers to the “gradient” or “slant” of a lineMethod OneGradient Formula
m=riserunTo find the gradient (m), measure the rise and run between two points on the lineFrom point (−1,0) to (0,2) the rise is 2 units and the run is 1 unitm = riserun = 21 m = 2 m=2Method TwoGradient Formula
m=y2−y1x2−x1First, choose any two coordinates on the line to use in the Gradient FormulaWe have chosen the points: (0,2) and (−1,0)Label the coordinates we chose from above(0,2)=(x1,y1)(−1,0)=(x2,y2)Solve for the gradient (m) by substituting the two coordinates into the formulam = y2−y1x2−x1 Gradient Formula = 0−2−1−0 Plug in the coordinates = −2−1 Evaluate m = 2 −2÷−1=2 m=2 -
Question 4 of 9
4. Question
Find the gradient of the line shown below- m= (2)
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The gradient (m) refers to the “gradient” or “slant” of a lineGradient Formula
m=riserunTo find the gradient (m), measure the rise and run between two points on the lineFrom point (0,0) to (1,2) the rise is 2 units and the run is 1 unitm = riserun = 21 m = 2 m=2 -
Question 5 of 9
5. Question
Find the gradient of the line shown below- m= (1)
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Chapters- Chapters
The gradient (m) refers to the “gradient” or “slant” of a lineGradient Formula
m=riserunTo find the gradient (m), measure the rise and run between two points on the lineFrom point (0,0) to (2,2) the rise is 2 units and the run is 2 unitsm = riserun = 22 m = 1 m=1 -
Question 6 of 9
6. Question
Find the gradient of the line shown below- m= (1/4, 0.25)
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The gradient (m) refers to the “gradient” or “slant” of a lineGradient Formula
m=riserunTo find the gradient (m), measure the rise and run between two points on the lineFrom point (0,0) to (4,1) the rise is 1 unit and the run is 4 unitsm = riserun = 14 m = 14 m=14 -
Question 7 of 9
7. Question
Find the gradient of the line shown below- m= (-1/2, -0.5)
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The gradient (m) refers to the “gradient” or “slant” of a lineGradient Formula
m=riserunTo find the gradient (m), measure the rise and run between two points on the lineFrom point (4,0) to (0,2) the rise is 2 units and the run is −4 unitsm = riserun = 2−4 = −24 m = −12 Reduce to lowest terms m=−12 -
Question 8 of 9
8. Question
Is the shape below a parallelogram?- 1.
-
2.
No
Hint
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A parallelogram is a quadrilateral with opposite sides parallel. Parallel lines have the same gradients.Gradient Formula
m=y2−y1x2−x1First, label the given coordinatesA(1,2)=(x1,y1)B(5,2)=(x1,y1)C(3,−2)=(x2,y2)D(−1,−2)=(x2,y2)Solve for the gradient (m) by substituting the pairs of coordinates for lines AD and BC into the formulamAD = y2−y1x2−x1 = −2−2−1−1 = −4−2 mAD = 2 mBC = y2−y1x2−x1 = −2−23−5 = −4−2 mBC = 2 Identify whether the quadrilateral is a parallelogram.mAD=mBC so lines AD and BC are parallel, and therefore the given quadrilateral is a parallelogram.The quadrilateral is a parallelogram. -
Question 9 of 9
9. Question
Are the two lines parallel?-
1.
No -
2.
Yes
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Parallel lines have the same gradients.Gradient Formula
m=riserunTo find the gradient (m), measure the rise and run between two points on the lineBlack line: From point (4,0) to (0,4) the rise is 4 units and the run is −4 unitsm = riserun = 4−4 m = −1 Red line: From point (−2,0) to (0,−2) the rise is −2 units and the run is 2 unitsm = riserun = −22 m = −1 The two gradients are equal, so the lines are parallel.The lines are parallel. -
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Quizzes
- Distance Between Two Points 1
- Distance Between Two Points 2
- Distance Between Two Points 3
- Midpoint of a Line 1
- Midpoint of a Line 2
- Midpoint of a Line 3
- Gradient of a Line 1
- Gradient of a Line 2
- Gradient Intercept Form: Graph an Equation 1
- Gradient Intercept Form: Graph an Equation 2
- Gradient Intercept Form: Write an Equation 1
- Determine if a Point Lies on a Line
- Graph Linear Inequalities 1
- Graph Linear Inequalities 2
- Convert Between General Form and Gradient Intercept Form 1
- Convert Between General Form and Gradient Intercept Form 2
- Point Gradient and Two Point Formula 1
- Point Gradient and Two Point Formula 2
- Parallel Lines 1
- Parallel Lines 2
- Perpendicular Lines 1
- Perpendicular Lines 2