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The following values of x and y are thought to satisfy a linear equation:
x 1 2
y 1 3
Draw the graph, using the values of x, y as given in the above table. At what point the graph of the linear equation (i) cuts the x-axis. (ii) cuts the y-axis

Solution:

Given, the table represents the values of x and y that satisfy a linear equation.

We have to draw the graph using the values and find the points at which the equation cuts the x-axis and the y-axis.

The linear equation of a line is given by

y = mx + c

Where, m is the slope

c is the y-intercept.

To find slope use the formula,

m = (y₂ - y₁) / (x₂ - x₁)

Given, x₂ = 2, x₁ = 1, y₂ = 3 and y₁ = 1

m = (3 - 1) / (2 - 1)

m = 2

Using the point (1, 1)

(1) = 2(1) + c

1 = 2 + c

c = 1 - 2

c = -1

Put m = 2 and c = -1 in the equation,

y = (2)x + (-1)

y = 2x - 1

Therefore, the linear equation is y = 2x - 1

The graph cuts the x-axis when y = 0

Put y = 0 in the linear equation

0 = 2x - 1

2x = 1

x = 1/2

Therefore, the graph cuts the x-axis at the point (1/2, 0)

The graph cuts the y-axis at x = 0

Put x = 0 in the linear equation

y = 2(0) - 1

y = -1

Therefore, the graph cuts the y-axis at the point (0, -1)

✦ Try This: The following values of x and y are thought to satisfy a linear equation:

x 1 2
y 2 4

Draw the graph, using the values of x, y as given in the above table. At what point the graph of the linear equation (i) cuts the x-axis. (ii) cuts the y-axis?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 4

NCERT Exemplar Class 9 Maths Exercise 4.4 Sample Problem 2

The following values of x and y are thought to satisfy a linear equation: x 1 2 y 1 3. Draw the graph, using the values of x, y as given in the above table. At what point the graph of the linear equation (i) cuts the x-axis, (ii) cuts the y-axis

Summary:

The graph using the values of x, y as given in the table is mentioned above. The point at which the graph of the linear equation (i) cuts the x-axis is (1/2, 0), (ii) cuts the y-axis is (0, -1)

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