Question

Give the geometric representations of the following equations

(a) on the number line (b) on the Cartesian plane:

$\left(i\right)x=2$ $\left(ii\right)y+3=0$ $\left(iii\right)y=3$ $\left(iv\right)2x+9=0$ $\left(v\right)3x-5=0$

Answer 1

$\left(i\right)x=2$

a) On the number line

b) x = 2 is a line parallel to y-axis at a distance of 2 units tothe right of y-axis.

$\left(ii\right)y+3=0\Rightarrow y=-3$
a) On the number line

b) y = - 3 is a line parallel to x-axis at a distance of 3 units below x-axis.

$\left(iii\right)y=3$
a) On the number line

b) y = 3 is a line parallel to x-axis at a distance of 3 units above x-axis.

$\left(iv\right)2x+9=0\Rightarrow 2x=-9\Rightarrow x=\frac{-9}{2}=-4.5$

a) On the number line

x = -4.5 is a line parallel to y-axis at a distance of 4.5 units to left of y-axis.

$\left(v\right)3x-5=0\Rightarrow 3x=5\Rightarrow x=\frac{5}{3}=1\frac{2}{3}$

a) On the number line

$b)x=1\frac{2}{3}\text{is a line parallel to y-axis at a distance of}1\frac{2}{3}\text{unit to right side of y-axis.}$