Graphs

Linear formulas and equations: Formulas

Graphs

Graph

We can create a table corresponding to the formula $\blue{y=5x+10}$ :

$\begin{array}{l|c|c|c|c|c} x & 0 & 1 & 2 & 3 & 4\\ \hline y & 10 & 15 & 20 & 25 & 30 \end{array}$ We made this table by calculating the value of $y$ corresponding to the chosen value of $x$ in the upper row. The values of $y$ are in the bottom row.

We can make a graph corresponding to this table. The upper row with values for $x$ corresponds to the horizontal axis, and the bottom row with values for $y$ corresponds to the vertical axis.

If $x=1$ , then $y=15$ . This corresponds to the point $\rv{1,15}$ . On the right, you can find this point by drawing perpendicular lines from the axes. From the table, it follows that the graph goes through the following points: $\rv{0,10}$ , $\rv{1,15}$ , $\rv{2,20}$ , $\rv{3,25}$ and $\rv{4,30}$ . These points are drawn on the right and connected by a smooth line, which, in this case, is a straight line.

Draw a graph corresponding to the formula:
$y=\left(x-5\right)\cdot \left(x-1\right)\cdot \left(x+2\right)$

First of all, we compose a table corresponding to the graph. For this we substitute the $x$ -values in the formula. For $x=-4$ we find $y=\left(-4-5\right)\cdot \left(-4-1\right)\cdot \left(-4+2\right)=-90$ . The other $x$ -values follow the same pattern. We eventually find the table below.

$\boldsymbol{x}$	$-4$	$-3$	$-2$	$-1$	$0$	$1$	$2$	$3$	$4$
$\boldsymbol{y}$	$-90$	$-32$	$0$	$12$	$10$	$0$	$-12$	$-20$	$-18$

To compose the graph, we draw a coordinate system. Then, we draw the points from the table in the coordinate system because these are points in the graph. The $x$ -value is on the horizontal axis, and the $y$ -value is on the vertical axis. We then connect these points with a smooth curve, giving us the graph below. The points from the table are coloured red.

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