Linear GraphsCambridge IGCSE Maths: Flashcards

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State the general equation of a straight line.

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State the general equation of a straight line.: $y = mx + c$ , where $m$ is the gradient and $c$ is the $y$ -intercept.
What does $c$ represent in $y=mx+c$ ?: The $y$ -intercept, i.e. the value of $y$ when $x=0$ .
State the formula for the gradient through two points $(x_1,y_1)$ and $(x_2,y_2)$ .: $m=\dfrac{y_2-y_1}{x_2-x_1}$
Find the gradient of the line through $(1,3)$ and $(4,9)$ .: $m=\dfrac{9-3}{4-1}=2$
Rearrange $2x+3y=12$ into $y=mx+c$ form.: $y=-\dfrac{2}{3}x+4$
What is true of two parallel lines' gradients?: They are equal.
What is the relationship between the gradients of perpendicular lines?: $m_1 \times m_2 = -1$
Find the gradient of a line perpendicular to a line with gradient 5.: $m_2 = -\dfrac{1}{5}$
Find the equation of the line parallel to $y=4x-1$ passing through $(1,-3)$ .: $y=4x-7$
What is a perpendicular bisector of a line segment?: A line perpendicular to the segment that passes through its midpoint.
Find the equation of the line through $(2,7)$ with gradient 3.: $y=3x+1$
What method finds the equation of a line given a point and gradient?: Substitute the point's coordinates and the gradient into $y=mx+c$ , then solve for $c$ .
What common mistake occurs when finding a perpendicular gradient?: Forgetting to both flip (reciprocal) and negate the original gradient.
What does 'Core' vs 'Extended' differ on for finding gradients?: Core finds gradient from a grid; Extended finds it algebraically from two coordinate points.
What form does Extended use besides $y=mx+c$ for a straight-line equation?: $ax+by=c$