Gradient of a Line Flashcards

All 6 cards in this deck

What does the gradient of a straight line measure?

Its steepness — how much $y$ changes for every $1$ that $x$ increases.

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

gradient $= \dfrac{y_2-y_1}{x_2-x_1}$ (change in $y$ $\div$ change in $x$)

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

e.g. $(1, 2)$ and $(4, 8)$

1. Change in $y$: $8 - 2 = 6$.
2. Change in $x$: $4 - 1 = 3$.
3. Divide: $6 \div 3 = 2$, so the gradient is $2$.

True or false? To find a gradient you divide the change in $x$ by the change in $y$.

False.

It is change in $y$ divided by change in $x$.

True or false? A line sloping downwards from left to right has a negative gradient.

True.

$y$ decreases as $x$ increases.

What are the steps to find a missing coordinate when you know the gradient and one point?

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

1. Put the values into the gradient formula: $\dfrac{15-9}{d-5} = 3$.
2. Rearrange: $6 = 3(d-5)$, so $d - 5 = 2$.
3. $d = 7$.