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A day full of math games & activities. Find one near you.

The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation:
x 6 -6
y -2 6
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 = -6, x₁ = 6, y₂ = 6 and y₁ = -2

m = (6 + 2) / (-6 - 6)

m = 8/-12

m -2/3

Using the point (6, -2)

-2 = (-2/3)6 + c

-2 = -2(2) + c

-2 = -4 + c

c = 4 - 2

c = 2

Put m = -2/3 and c = 2 in the equation,

y = (-2/3)x + 2

3y = -2x + 6

2x + 3y = 6

Therefore, the linear equation is 2x + 3y = 6

The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation x 6 -6 y -2 6. 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

The graph cuts the x-axis when y = 0

Put y = 0 in the linear equation

2x + 3(0) = 6

2x = 6

x = 6/2

x = 3

Therefore, the graph cuts the x-axis at the point (3, 0)

The graph cuts the y-axis at x = 0

Put x = 0 in the linear equation

2(0) + 3y = 6

3y = 6

y = 6/3

y = 2

Therefore, the graph cuts the y-axis at the point (0, 2)

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

x 1 4
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 Problem 2

The following observed values of x and y are thought to satisfy a linear equation. Write the linear equation: x 6 -6 y -2 6. 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 linear equation for the values of x and y given in the above table is 2x + 3y = 6. The points at which the graph of the linear equation (i) cuts the x-axis is (3, 0), (ii) cuts the y-axis is (0, 2)

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