:"1.3.1 Coordinate geometry in the (x, y) plane Flashcards","topicId":"b3cb6ee6-fd5f-47cd-9a1d-8c5fc56709fd","topicSlug":"coordinate-geometry-in-the-x-y-plane-2","cards":[{"id":"b2e5b6ea-15ce-465e-8d4f-2753e3b6b00a","cardType":"cloze","front":"

The gradient between $A(x_1,y_1)$ and $B(x_2,y_2)$ is $\\text{[...]}$.

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The gradient between $A(x_1,y_1)$ and $B(x_2,y_2)$ is $\\boxed{m=\\frac{y_2-y_1}{x_2-x_1}}$.

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What does a positive gradient show?

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The line rises from left to right.

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What does a negative gradient show?

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The line falls from left to right.

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Why is the gradient of a vertical line undefined?

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The change in $x$ is zero, causing division by zero.

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What equation form represents a vertical line through $x=k$?

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$x=k$

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What equation form represents a horizontal line through $y=k$?

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$y=k$

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In $y=mx+c$, $m$ is the [ ] and $c$ is the $y$-intercept.

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In $y=mx+c$, $m$ is the gradient and $c$ is the $y$-intercept.

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In $y=mx+c$, $m$ is the gradient and $c$ is the [ ].

","back":"

In $y=mx+c$, $m$ is the gradient and $c$ is the $y$-intercept.

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What are the gradient and $y$-intercept of $y=-3x+8$?

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Gradient: $-3$
$y$-intercept: $8$

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A line with gradient $m$ through $(x_1,y_1)$ has point-gradient equation $\\text{[...]}$.

","back":"

A line with gradient $m$ through $(x_1,y_1)$ has point-gradient equation $\\boxed{y-y_1=m(x-x_1)}$.

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Find the equation of the line with gradient $4$ through $(3,-5)$.

","back":"

$y=4x-17$

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Find the gradient of the line through $(-2,5)$ and $(4,-7)$.

","back":"

$m=-2$

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What happens if only one coordinate difference is reversed in the gradient formula?

","back":"

The gradient's sign changes incorrectly.

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The gradient of $ax+by+c=0$, where $b\\neq0$, is $\\text{[...]}$.

","back":"

The gradient of $ax+by+c=0$, where $b\\neq0$, is $\\boxed{m=-\\frac{a}{b}}$.

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Find the gradient of $3x+2y-10=0$.

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$-\\frac{3}{2}$

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