AQA · Mathematics · 8300
GCSE Maths: Linear graphs: parallel lines
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Linear graphs: parallel lines (Corbettmaths Video 196), 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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? lines have the same gradient.
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Parallel
What is the gradient of a line parallel to y = 7x + 4?
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7
What is the equation of a line parallel to y = 3x + 5 and passing through (0, 2)?
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y = 3x + 2
What is the negative reciprocal of 4?
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−¼ (or −0.25)
The gradient of a line perpendicular to another is the ? of the original gradient.
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negative reciprocal
What is the gradient of a line perpendicular to y = 2x + 4?
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−½
Are the lines 2x + y = 8 and y = 2x + 5 parallel?
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No. The first line has gradient −2 (rearranged: y = −2x + 8), while the second has gradient 2.
Are the lines 4x − y − 5 = 0 and x + 4y + 1 = 0 perpendicular?
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Yes. Their gradients are 4 and −¼, which are negative reciprocals.
What is the equation of a line perpendicular to y = 2x − 1 and passing through (0, 3)?
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y = −½x + 3
If a line passes through (0, 6) and (4, −2), what is its gradient?
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−2 (calculated as (−2 − 6) ÷ (4 − 0) = −8 ÷ 4)
What is the equation of a line parallel to x + 2y = 4 and passing through (0, 5)?
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y = −½x + 5 (or x + 2y = 10)
In the equation y = mx + c, the coefficient m represents the ?.
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gradient
In the equation y = mx + c, the constant c represents the ?.
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y-intercept
What is the formula for calculating the gradient of a line passing through points (x₁, y₁) and (x₂, y₂)?
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Gradient = (y₂ − y₁) / (x₂ − x₁)
What is the first step to find the equation of a line parallel to a given line and passing through a specific point?
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Identify the gradient of the given line, since parallel lines have the same gradient.
How do you rearrange the equation 8x − 2y = 3 into the form y = mx + c?
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Isolate y: −2y = −8x + 3, then divide by −2 to get y = 4x − 3/2.
To show that two lines are parallel, what must you demonstrate about their equations?
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That they have the same gradient when written in the form y = mx + c.
If line A passes through (−3, 4) and (3, 7), and line B is parallel to A and passes through (1, 0) and (10, p), how would you find p?
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Calculate gradient of A, then use the same gradient for B to find p: gradient of A = gradient of B.
Where does a line cross the x-axis?
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At the point where y = 0.
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