Recognise a line or find points for its graph

The rule y=2x+1 gives the pair (2,5). Which movement locates it from the origin?

Move x through −2, 0, 2 and 3. Match each readout pair to the plotted point and the dashed guides

What remains true for every marked point?

Data

\(\displaystyle y=2x+1,\quad x=-1\)

Find the output for x=−1 in y=2x+1.

Data

\(\displaystyle y=2x+1,\quad x=2\)

Find the output for x=2 in the same rule

A(−1,−1) and B(2,5) are plotted. Why is a third point useful?

From a rule to a line

Choose convenient inputs, calculate their outputs and plot each pair using both numerical scales

1. 1Calculate Include negative signs and evaluate multiplication first
2. 2Plot Move to x horizontally, then to y vertically. Read labels rather than counting unlabelled squares
3. 3Check Use two distinct points and calculate another point independently
4. 4Join appropriately For an unrestricted linear equation, use a straight ruled line. A context may restrict the graph to a segment or separate points

Data

\(\displaystyle y=3-\frac{x}{2},\quad x=4\)

For y=3−x/2, find the y-coordinate of the point with x=4.

Data

\(\displaystyle 2y+x=6,\quad x=-2\)

For 2y+x=6, find y when x=−2.

A horizontal scale has 2 units per grid interval and the vertical scale has 5. A point is 3 intervals right and 2 intervals up from the origin. What are its coordinates?

A student records (0,1) twice for y=2x+1. Have they found two points that determine the line?

Which proposed point fails the rule y=2x+1?

A table for y=2x+1 lists (0,1),(1,3),(2,5). Should an unrestricted graph stop at these three dots?