Straight lines
Practice Flashcards
What is the gradient formula?
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All Flashcards in Topic 2.1
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2.1.110 cards
What is the gradient formula?
m = (y₂ − y₁)/(x₂ − x₁) = rise ÷ run. Subtract the coordinates in the same order top and bottom.
What does the sign of the gradient tell you?
m > 0 uphill, m < 0 downhill, m = 0 horizontal (y = c), vertical lines (x = a) have no gradient.
State the three forms of a straight line.
Gradient–intercept y = mx + c; point–gradient y − y₁ = m(x − x₁); general ax + by + d = 0.
In y = mx + c, what are m and c?
m is the gradient; c is the y-intercept (where the line crosses the y-axis).
How do you get the gradient from ax + by + d = 0?
Rearrange to y = mx + c — the gradient is m = −a/b.
How do you find a line from a gradient m and a point (x₁, y₁)?
Use point–gradient form y − y₁ = m(x − x₁), then expand and tidy.
How do you find a line through two points?
Find the gradient m = (y₂ − y₁)/(x₂ − x₁) first, then use point–gradient form with either point.
How do you find the y-intercept of a line?
Set x = 0 (or, in y = mx + c, read off c).
How do you find the x-intercept of a line?
Set y = 0 and solve for x.
What are the equations of vertical and horizontal lines?
Vertical: x = a (gradient undefined). Horizontal: y = b (gradient 0).
2.1.210 cards
When are two lines parallel?
When they have the same gradient: m₁ = m₂ (with different y-intercepts).
When are two lines perpendicular?
When their gradients multiply to −1: m₁m₂ = −1, i.e. m₂ = −1/m₁.
How do you get the perpendicular gradient?
Take the negative reciprocal — flip the fraction and change the sign. E.g. ⅔ → −3/2.
Perpendicular gradient of 5?
Write 5 as 5/1; the perpendicular gradient is −1/5.
How do you find a line through a point parallel to a given line?
Use the SAME gradient, then point–gradient form y − y₁ = m(x − x₁).
How do you find a line through a point perpendicular to a given line?
Use the negative-reciprocal gradient, then point–gradient form.
What is a perpendicular bisector?
The line through the midpoint of a segment, perpendicular to it (negative-reciprocal gradient).
Midpoint of (x₁, y₁) and (x₂, y₂)?
((x₁ + x₂)/2, (y₁ + y₂)/2) — average each coordinate.
What is a normal to a curve?
The line perpendicular to the tangent at a point; its gradient is −1/(tangent gradient). Used in calculus.
Why doesn't m₁m₂ = −1 work for horizontal & vertical lines?
They are perpendicular, but a vertical line (x = a) has no gradient, so the product rule can't be applied — state it separately.
Topic 2.1 study notes
Full notes & explanations for Straight lines
Math AA SL exam skills
Paper structures, command terms & tips
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