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

First equation: y = $\dfrac{3x + 2}{2}$

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -4, then y = $\dfrac{3 \times (-4) + 2}{2}$ ⇒ y = -5

Let x = -2, then y = $\dfrac{3 \times (-2) + 2}{2}$ ⇒ y = -2

Let x = 2, then y = $\dfrac{3 \times 2 + 2}{2}$ ⇒ y = 4

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

Second equation: y = $\dfrac{3}{4}x - 2$

Step 1:

Give at least three suitable values to the variable x and find the corresponding values of y.

Let x = -4, then y = $\dfrac{3}{4} \times (-4) - 2$ ⇒ y = -5

Let x = 4, then y = $\dfrac{3}{4} \times 4 - 2$ ⇒ y = 1

Let x = 8, then y = $\dfrac{3}{4} \times 8 - 2$ ⇒ y = 4

Step 2:

Make a table (as given below) for the different pairs of the values of x and y:

Step 3:

Plot the points, from the table, on a graph paper and then draw a straight line passing through the points plotted on the graph.

After plotting both lines on the graph, observe where the two lines intersect. The intersection point represents the value of x where both equations are equal.

From the graph, we see that the lines intersect at x = -4.

Hence, the value of x for which the two equations are equal is -4.