Drawing Straight Line Graphs Flashcards

All 5 cards in this deck

What are the steps to complete a table of values for a linear equation?

e.g. $y = 4x - 6$ for $x = -1, 0, 1$

1. Substitute the first $x$ value into the equation: $4 \times (-1) - 6 = -10$
2. Repeat for each $x$ value: $x = 0$ gives $-6$, $x = 1$ gives $-2$
3. Write each $y$ value under its $x$ value

What are the steps to draw the graph of $y = mx + c$ over a given range of $x$?

e.g. $y = \frac{1}{2}x - 1$ for $x$ from $-2$ to $3$

1. Complete a table of values: $y = -2, -1.5, -1, -0.5, 0, 0.5$
2. Plot the points, e.g. $(-2, -2)$ and $(3, 0.5)$
3. Join them with a single ruled straight line from $x = -2$ to $x = 3$

What does the graph of $x = -2$ look like?

A vertical line through $(-2, 0)$, parallel to the $y$-axis.

Every point on it has $x$-coordinate $-2$.

What does the graph of $y = -3$ look like?

A horizontal line through $(0, -3)$, parallel to the $x$-axis.

Every point on it has $y$-coordinate $-3$.

How do you find the gradient of a straight line drawn on a grid?

e.g. a line passing through $(1, 2)$ and $(4, 8)$

Gradient $= \frac{\text{change in } y}{\text{change in } x}$ between two points on the line.

$\frac{8-2}{4-1} = 2$