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

All 6 cards in this deck

What is the gradient of a line with equation $y = mx + c$?

e.g. $y = 2x + 3$

$m$, the coefficient of $x$.

So $y = 2x + 3$ has gradient $2$.

What are the coordinates of the point where the line $y = mx + c$ crosses the $y$-axis?

e.g. $y = -4x + 3$

$(0, c)$.

So $y = -4x + 3$ crosses at $(0, 3)$.

What are the steps to find the gradient of a line whose equation is not in the form $y = mx + c$?

e.g. $3y - 9x = 6$

1. Get the $y$ term alone: $3y = 9x + 6$
2. Divide every term by the number in front of $y$: $y = 3x + 2$
3. The gradient is the coefficient of $x$: $3$

What are the steps to find the equation of the line through two given points?

e.g. through $(0, 3)$ and $(2, -1)$

1. Gradient $m = \frac{\text{change in } y}{\text{change in } x} = \frac{-1-3}{2-0} = -2$
2. Find $c$ from a point on the line: the line crosses the $y$-axis at $(0,3)$, so $c = 3$
3. Write $y = mx + c$: $y = -2x + 3$

What are the steps to find the equation of a line through one point with a given gradient?

e.g. gradient $4$ through $(2, 9)$

1. Write $y = mx + c$ with the gradient: $y = 4x + c$
2. Substitute the point's coordinates: $9 = 4 \times 2 + c$
3. Solve for $c$ and write the equation: $c = 1$, so $y = 4x + 1$

How do you check algebraically whether a point lies on a given straight line?

e.g. does $(2, 9)$ lie on $y = 4x + 1$?

Substitute the $x$-coordinate into the equation and see if you get the $y$-coordinate.

$4 \times 2 + 1 = 9$, so yes, $(2, 9)$ lies on the line.