Equations of Straight Lines (y = mx + c) Flashcards

All 5 cards in this deck

In the equation $y = mx + c$, what do $m$ and $c$ stand for?

$m$ is the gradient and $c$ is the $y$-intercept (where the line crosses the $y$-axis).

What is the formula for the gradient of the line through two points?
e.g. $(1, 2)$ and $(4, 8)$

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$
e.g. $\dfrac{8-2}{4-1} = 2$

What are the steps to rearrange an equation into the form $y = mx + c$ and state the gradient and intercept?
e.g. $3y - 9x + 5 = 0$

1. Get the $y$ term alone: $3y = 9x - 5$
2. Divide every term by the coefficient of $y$: $y = 3x - \frac{5}{3}$
3. Read off: gradient $3$, $y$-intercept $-\frac{5}{3}$

What are the steps to find the equation of the line through two given points?
e.g. $(1, 5)$ and $(3, 11)$

1. Gradient $= \frac{11-5}{3-1} = 3$
2. Substitute one point into $y = 3x + c$: $5 = 3 + c$, so $c = 2$
3. Equation: $y = 3x + 2$

What are the steps to find the equation of a line with a given gradient through a given point?
e.g. gradient $4$ through $(2, 5)$

1. Write $y = 4x + c$
2. Substitute the point: $5 = 4 \times 2 + c$, so $c = -3$
3. Equation: $y = 4x - 3$ (or $y - 5 = 4(x - 2)$)