AQA · Mathematics · 8300
GCSE Maths: Linear graphs: perpendicular lines
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise, practice questions and answers for Linear graphs: perpendicular lines (Corbettmaths Video 197), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the relationship between the gradients of two parallel lines?
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Parallel lines have equal gradients (the same slope).
What is the relationship between the gradients of two perpendicular lines?
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The gradients are negative reciprocals of each other. If one line has gradient m, the perpendicular line has gradient −1/m.
A line is parallel to y = 5x − 3 and passes through (0, 7). What is its equation?
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y = 5x + 7. Parallel lines have the same gradient, and passing through (0, 7) means the y-intercept is 7.
A line is perpendicular to y = 2x + 4. What is its gradient?
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−½. The gradient is the negative reciprocal of 2.
What is the negative reciprocal of ⅔?
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−3/2. Flip the fraction and change the sign.
A line passes through (0, k). What does k represent in the equation y = mx + c?
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k is the y-intercept (c in the equation). The line crosses the y-axis at (0, k).
Are the lines y = 2x + 3 and y = 2x − 5 parallel or perpendicular?
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Parallel. They have the same gradient (2) but different y-intercepts.
If a line has equation y = mx + c, what does m represent?
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m represents the gradient (or slope) of the line.
If a line has gradient m, what is the gradient of a line perpendicular to it?
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−1/m (the negative reciprocal)
To find the equation of a perpendicular line through a given point, first find the perpendicular gradient, then substitute the point into ? to find c.
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y = mx + c
What are the two steps to find a line perpendicular to AB that passes through a given point?
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1) Calculate the gradient of AB and find its negative reciprocal. 2) Use the point to find c in y = mx + c.
What is the gradient of a line perpendicular to y = −(2/3)x?
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3/2
How do you show that angle ABC is a right angle using coordinate geometry?
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Calculate the gradients of AB and BC. If their product equals −1, then the lines are perpendicular and angle ABC is a right angle.
To find the gradient of a line from the equation 5x − 2y + 4 = 0, what must you do first?
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Rearrange the equation into the form y = mx + c (where m is the gradient)
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