Linear Graphs (y = mx + c)Edexcel IGCSE Maths: Flashcards

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What does $m$ represent in $y = mx + c$?

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What does $m$ represent in $y = mx + c$ ?: The gradient (steepness and direction) of the line.
What does $c$ represent in $y = mx + c$ ?: The y-intercept — the point $(0, c)$ where the line crosses the y-axis.
What is the formula for the gradient between two points $(x_1,y_1)$ and $(x_2,y_2)$ ?: $m = \dfrac{y_2-y_1}{x_2-x_1}$
Find the gradient through $(0,1)$ and $(2,7)$ .: $m = \dfrac{7-1}{2-0} = 3$
What is the condition for two lines to be parallel?: They have equal gradients: $m_1 = m_2$ .
What is the condition for two lines to be perpendicular?: Their gradients multiply to $-1$ : $m_1 \times m_2 = -1$ .
If a line has gradient 5, what is the gradient of a line perpendicular to it?: $-\dfrac{1}{5}$
If a line has gradient $-\dfrac{2}{3}$ , what is the gradient of a perpendicular line?: $\dfrac{3}{2}$
What is the equation of a horizontal line through $(4, 7)$ ?: $y = 7$
What is the equation of a vertical line through $(4, 7)$ ?: $x = 4$
What is the gradient of any horizontal line?: 0
What is the gradient of any vertical line?: Undefined
Given $m = 3$ and the point $(2,5)$ lies on the line, find $c$ .: $5 = 3(2) + c \Rightarrow c = -1$
What is the point-gradient form of a line's equation?: $y - y_1 = m(x - x_1)$
Rearrange $2y = 4x + 6$ into $y = mx + c$ form and state $m$ .: $y = 2x + 3$ , so $m = 2$