Question

Draw the graphs of the equations $x-y+1=0$ and $3x+2y-12=0$. Determine the coordinates of the vertices of the triangle formed by these lines and the $x$-axis and shade the triangular region.

Answer 1

Solution:

From the given, the equations for graphs are$x-y+1=0$ and $3x+2y-12=0$

Step 1: Finding the table from the equation $x-y+1=0$

For, $x-y+1=0ory=x+1$

$x$	$0$	$1$	$2$
$y$	$1$	$2$	$3$

Step 2: Finding the table from the equation $3x+2y-12=0$

For, $3x+2y-12=0ory=\frac{1}{2}(12-3x)$

$x$	$4$	$2$	$0$
$y$	$0$	$3$	$6$

Step 3: Drawing the graph of equations by taking values from the respective table

The graphical representation of the equations is

From the figure, we notice that these lines are intersecting each other at point $(2,3)\&x-axisat(-1,0)\&(4,0).$

Hence, the vertices of the triangle are $(2,3),(-1,0)\&(4,0)$