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Flip to reveal answersWhat is the gradient formula?
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All 10 Flashcards — Equations of lines
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Question
What is the gradient formula?
Answer
m = (y₂ − y₁)/(x₂ − x₁) = rise ÷ run. Subtract the coordinates in the same order top and bottom.
Question
What does the sign of the gradient tell you?
Answer
m > 0 uphill, m < 0 downhill, m = 0 horizontal (y = c), vertical lines (x = a) have no gradient.
Question
State the three forms of a straight line.
Answer
Gradient–intercept y = mx + c; point–gradient y − y₁ = m(x − x₁); general ax + by + d = 0.
Question
In y = mx + c, what are m and c?
Answer
m is the gradient; c is the y-intercept (where the line crosses the y-axis).
Question
How do you get the gradient from ax + by + d = 0?
Answer
Rearrange to y = mx + c — the gradient is m = −a/b.
Question
How do you find a line from a gradient m and a point (x₁, y₁)?
Answer
Put m into y = mx + c, then substitute the point to find c. (Or use point–gradient form y − y₁ = m(x − x₁).)
Question
How do you find a line through two points?
Answer
Find the gradient m = (y₂ − y₁)/(x₂ − x₁) first, then substitute one point into y = mx + c to find c.
Question
How do you find the y-intercept of a line?
Answer
Set x = 0 (or, in y = mx + c, read off c).
Question
How do you find the x-intercept of a line?
Answer
Set y = 0 and solve for x.
Question
What are the equations of vertical and horizontal lines?
Answer
Vertical: x = a (gradient undefined). Horizontal: y = b (gradient 0).
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Full study notes for Equations of lines
Topic 2.1 hub
Straight lines
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