Flashcards · Maths · Graphs
Equations of Straight Lines
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How do you find the equation of a line through two points?
Find the gradient, substitute a point to find \(c\), then write \(y = mx + c\).
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What is the formula for the midpoint of two points?
\(\left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)\).
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What is the midpoint of \((2, 1)\) and \((6, 9)\)?
\((4, 5)\).
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What is true about the gradients of parallel lines?
They are equal.
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What is the equation of a line with gradient 3 through \((2, 9)\)?
\(y = 3x + 3\).
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What is the gradient of \(2y - 4x = 6\)?
2, because it rearranges to \(y = 2x + 3\).
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What do the gradients of perpendicular lines multiply to (Higher tier)?
\(-1\).
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What is the gradient perpendicular to 2 (Higher tier)?
\(-\dfrac{1}{2}\).
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What is the gradient perpendicular to \(-\dfrac{3}{4}\) (Higher tier)?
\(\dfrac{4}{3}\).
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How do you find where a line crosses the y-axis?
Put \(x = 0\).
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How do you find where a line crosses the x-axis?
Put \(y = 0\).
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Where does \(3x + 2y = 12\) cross the axes?
\((0, 6)\) and \((4, 0)\).
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How do you find the length of a line segment (Higher tier)?
Use Pythagoras with the change in \(x\) and the change in \(y\).
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What is the gradient of the line through \((2, 1)\) and \((6, 9)\)?
2.
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How can you check an equation you have found?
Put the other point into it.
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If the midpoint and one end are known, how do you find the other end?
Double the midpoint and subtract the end you know.