C3.2 Drawing linear graphs

Learning objectives

C3.2.1Draw straight-line graphs for linear equations• Draw straight-line graphs for linear equations. Equations will be given in the form y = mx + c (e.g. y = –2x + 5), unless a table of values is given.

Every pair $(x,y)$ satisfying a linear equation lies on one straight line. Generate accurate pairs, plot them, then use a ruler to draw the line.

Read both axis scales; choose at least two well-separated $x$ -values in the required interval; substitute each into the equation; plot every resulting $(x,y)$ pair; check the points align; draw one ruled line through them across only the stated interval.

$y=8-2x,\qquad 0\le x\le4$

$x$	$0$	$2$	$4$
$y=8-2x$	$8$	$4$	$0$

Plot $(0,8)$ , $(2,4)$ and $(4,0)$ . A ruled segment through all three points is the graph for $0\le x\le4$ . The middle point checks that the endpoint calculations are consistent.

Equation	What to draw
$y=k$	a horizontal line through $y=k$
$y=x$	points with equal coordinates, such as $(-2,-2)$ and $(3,3)$

For $y=mx+c$ , setting $x=0$ gives the point $(0,c)$ . Increasing $x$ by 1 changes $y$ by $m$ , so the plotted points should follow that repeated change.

Do not join points freehand or stop at isolated dots when a graph is requested. Use the axis scales—not the number of grid squares—to position each coordinate.

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—C3.3 Gradient of linear graphsRead