11.1 Coordinates and plotting graphs — Learn

Prerequisites: read ordered pairs and calculate with positive and negative integers.

Objectives

By the end of this section, you can plot points in four quadrants and plot a straight-line graph from a rule.

Coordinates and straight-line graphs

A coordinate is written $(x,y)$. The first value gives the horizontal position. The second gives the vertical position. The axes meet at the origin, $(0,0)$.

To plot a point, move along the horizontal axis first, then move vertically. A negative coordinate means move left or down.

Worked example. Plot $(-2,3)$ and find the values for $y=2x+1$ when $x=-1,0,1$.

For $(-2,3)$, move two units left and three units up.

Plot $(-1,-1)$, $(0,1)$ and $(1,3)$, then join the points with a straight line.

Watch out. Reversing the coordinates changes the point. For $(-2,3)$, $-2$ is horizontal and $3$ is vertical. Check both movements from the origin.

Progress check

The walker is at $(0,0)$ after 0 minutes and $(30,2)$ after 30 minutes. Plot both points. What does the horizontal coordinate measure?

Try a graph rule

Predict: for $y=2x+1$, predict $y$ when $x=2$. Test: use the figure to check. Explain: describe how changing $x$ changes $y$.

You should now be able to

• plot coordinates in all four quadrants;
• plot a straight-line graph from a rule;
• check plotted points against the equation.