Question

Use the graphical method to find the value of 'x' for which the expressions $\frac{3x+2}{2}$ and $\frac{3}{4}x-2$ are equal.

Answer 1

Let $y=\frac{3x+2}{2}$
Substituting different values of $x$, we get corresponding values of $y$
That is, $whenx=0,y=1;whenx=2,y=4;whenx=-2,y=-2$
Plotting these points on the graph, we get the graph of $y=\frac{3x+2}{2}$
Similarly,
Let $y=\frac{3x}{4}-2$
Substituting different values of $x$, we get corresponding values of $y$
That is, $whenx=0,y=-2;whenx=4,y=1;whenx=-4,y=-5$
Plotting these points on the graph, we get the graph of $y=\frac{3x}{4}-2$
From the graph, we see that the lines intersect at a point whose x - coordinate $x=-4$
Thus, at $x=-4$, the expressions are equal