**Graphing linear equations using intercepts :**

In this section, we are going to see, how linear equations can be graphed using intercepts.

The linear equation may be given in any form.(General form, Slope intercept form, Intercepts form, etc.,)

We have to do the following steps to graph a linear equation which may be given in any of the above forms.

**Step 1 : **

Finding x - intercept.

Substitute y = 0 in the given linear equation to find x - intercept.

For example, if you get x-intercept "a" (That is x = a), write this as a point (a, 0).

**Step 2 : **

Finding y - intercept.

Substitute x = 0 in the given linear equation to find y - intercept.

For example, if you get y-intercept "b" (That is y = b), write this as a point (0, b).

**Step 3 : **

Plot the points (a, 0) and (0, b) in xy-plane and connect them to get the graph (straight line) of the given linear equation.

**Example 1 :**

Graph the linear equation 2x - 3y + 6 = 0 using intercepts.

**Solution :**

**Step 1 : **

Find x-intercept.

Substitute y = 0 in the given equation.

2x - 3(0) + 6 = 0

2x + 6 = 0

Subtract 6 from both sides.

(2x + 6) - 6 = 0 - 6

2x = -6

Divide both sides by 2.

(2x)/2 = -6/2

x = -3

The point corresponding to the x-intercept "-3" is (-3, 0).

**Step 2 : **

Find y-intercept.

Substitute x = 0 in the given equation.

2(0) - 3y + 6 = 0

-3y + 6 = 0

Subtract 6 from both sides.

(-3y + 6) - 6 = 0 - 6

-3y = -6

Divide both sides by -3.

(-3y)/(-3) = (-6)/(-3)

y = 2

The point corresponding to the y-intercept "2" is (0, 2).

**Step 3 : **

Plot the two points (-3, 0) and (0, 2) in xy-plane and connect them to get the graph of the equation 2x - 3y + 6 = 0.

**Example 2 :**

Graph the linear equation y = (2/3)x - 4 using intercepts.

**Solution :**

**Step 1 : **

Find x-intercept.

Substitute y = 0 in the given equation.

0 = (2/3)x - 4

Add 4 to both sides.

0 + 4 = [(2/3)x - 4] + 4

4 = (2/3)x

Multiply both sides by 3/2.

(4)(3/2) = [(2/3)x](3/2)

6 = x

The point corresponding to the x-intercept "6" is (6, 0).

**Step 2 : **

Find y-intercept.

Substitute x = 0 in the given equation.

y = (2/3)(0) - 4

y = - 4

The point corresponding to the y-intercept "-4" is (0, -4).

**Step 3 : **

Plot the two points (6, 0) and (0, -4) in xy-plane and connect them to get the graph of the equation y = (2/3)x - 4.

After having gone through the stuff given above, we hope that the students would have understood "How to graph linear equations using intercepts".

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