Gradient of a Line Flashcards

All 7 cards in this deck

What is the formula for the gradient of the line joining $(x_1, y_1)$ and $(x_2, y_2)$?

$m = \dfrac{y_2 - y_1}{x_2 - x_1}$, i.e. the change in $y$ divided by the change in $x$.

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

e.g. $(1, 2)$ and $(4, 11)$

1. Change in $y$: $11 - 2 = 9$
2. Change in $x$: $4 - 1 = 3$
3. Divide: $9 \div 3 = 3$, so gradient $= 3$

What are the steps to find an unknown coordinate from a given gradient?

e.g. $A(5, 9)$, $B(d, 15)$, gradient of $AB$ is $3$

1. Put the coordinates into the gradient formula: $\dfrac{15-9}{d-5} = 3$
2. Multiply out: $6 = 3(d-5)$
3. Solve for the unknown: $d = 7$

What does a negative gradient tell you about a line?

It slopes downwards from left to right.

What is the gradient of a horizontal line?

$0$, because the change in $y$ is $0$.

True or false? A line of gradient $2$ is steeper than a line of gradient $-5$.

False. Steepness is judged by the size of the gradient ignoring the sign, so $-5$ is steeper.

Which coordinate calculation shows that two sides of a shape on coordinate axes are parallel?

Show the two sides have equal gradients.

e.g. gradient of $AB$ = gradient of $DC$ = $\frac{2}{3}$, so $AB$ is parallel to $DC$.