Draw the graph of straight line y = -2x + 3. Use your graph to find :

(i) the intercept on y-axis

(ii) the area between the line and co-ordinate axes.

Given equation: y = -2x + 3

Step 1:

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

Let x = 0, then y = -2 $\times$ 0 + 3 ⇒ y = 3

Let x = 1, then y = -2 $\times$ 1 + 3 ⇒ y = 1

Let x = 2, then y = -2 $\times$ 2 + 3 ⇒ y = -1

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.

(i) The y-intercept is the value of y when x = 0, which is 3.

Hence, the intercept on y-axis is 3.

(ii) The triangle formed by the line and coordinate axes has the following vertices:

A(0, 3), B(0, 0), C(1.5, 0)

Area of triangle ABC = $\dfrac{1}{2}$ x BC x AB

= $\dfrac{1}{2}$ x 1.5 x 3

= 2.25 sq. units

Hence, the area between the line and co-ordinate axes = 3.75 sq. units.