Flashcards · Maths · Graphs
Straight-Line Graphs
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What is the formula for the gradient of a line?
Gradient \(= \dfrac{\text{change in } y}{\text{change in } x}\).
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What does a positive gradient look like?
The line goes up from left to right.
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What does a negative gradient look like?
The line goes down from left to right.
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What does \(m\) mean in \(y = mx + c\)?
The gradient of the line.
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What does \(c\) mean in \(y = mx + c\)?
The \(y\)-intercept, where the line crosses the \(y\)-axis.
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What is the gradient of \(y = 5 - 3x\)?
\(-3\).
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What is the equation of a vertical line through 4 on the x-axis?
\(x = 4\).
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What is the equation of a horizontal line through 3 on the y-axis?
\(y = 3\).
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What is the equation of the x-axis?
\(y = 0\).
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What is the equation of the y-axis?
\(x = 0\).
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How do you know two lines are parallel from their equations?
They have the same gradient.
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How do you check whether a point is on a line?
Put its coordinates into the equation and see if both sides match.
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How can you sketch \(y = 2x + 1\) without a table?
Mark \((0, 1)\) and then go across 1 and up 2.
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Find the gradient of the line through \((1, 7)\) and \((4, 1)\).
\(\dfrac{1 - 7}{4 - 1} = -2\).
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Where does a line cross the x-axis?
Where \(y = 0\).
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How many points do you need to draw a straight line?
Two, but plot three to check.