E3.2 Drawing linear graphs

Learning objectives

E3.2.1Draw straight-line graphs for linear equations• Draw straight-line graphs for linear equations. Examples include: • y = –2x + 5 • y = 7 – 4x • 3x + 2y = 5.

A linear equation describes every point $(x,y)$ on one straight line. To draw the graph, find coordinate pairs that satisfy the equation, plot them accurately and join them with a ruled line.

Choose several convenient $x$ -values within the grid range.
Calculate the matching $y$ -value for each one. Rearrange first if necessary.
Plot the resulting $(x,y)$ points, using each axis scale correctly.
Check that the points line up, then draw one straight ruled line through them.

$3x+2y=5\quad\Longrightarrow\quad y=\frac{5-3x}{2}$

$x$	$-1$	$1$	$3$
$y=(5-3x)/2$	$4$	$1$	$-2$
point	$(-1,4)$	$(1,1)$	$(3,-2)$

For an equation such as $x+y=7$ , setting $x=0$ gives $(0,7)$ and setting $y=0$ gives $(7,0)$ . These two intercepts determine the line; an extra point is a useful check.

Substitute a plotted point back into the original equation. For $(3,-2)$ , $3(3)+2(-2)=5$ , so the point belongs on $3x+2y=5$ .

Two distinct correct points determine a straight line, but a third point helps reveal an arithmetic or plotting error. Do not draw separate segments, use a freehand curve, or confuse $x=7$ or $y=7$ with $x+y=7$ .

Next Topic

—E3.3 Gradient of linear graphsRead