Draw the graph of each of the following equations:

(i) x = 5

(ii) y = -2

(iii) x + 6 = 0

(iv) x + 7 = 0

(v) y = 0

(vi) x = 0

Draw the graph of the equation y = 3x. From you graph, find the value of y when x = -2.

Draw the graph of the equation x + 2y – 3 = 0. From your graph, find the value of y when x = 5.

Draw the graph of each of the following equations:

(i) y = x

(ii) y = -x

(iii) y + 3x = 0

(iv) 2x + 3y = 0

(v) 3x – 2y = 0

(vi) 2x +y =0

Draw the graph of the equation 2x - 3y = 5. From the graph, find (i) the value of y when x = 4, and (ii) the value of x when y = 3.

Draw the graph of the equation 2x + y = 6. Find the coordinates of the point, where the graph cuts the x-axis.

Draw the graph of the equation 3x + 2y = 6. Find the coordinates of the point, where the graph cuts the y-axis.

x = 0 is the equation of

y = 0 is the question of

x + 3 = 0 is the equation of a line

y – 4 = 0 is the equation of a line

The point of the form (a, a), where a ≠ 0 lies on

The point of the form (a, a), where a ≠ 0 lies on

The linear equation 3x – 5y = 15 has

The graph of the linear equation 3x + 2y = 6 cuts the y-axis at the point

The graph of the linear equation 4x + 3y = 12 cuts the x-axis at the point

The graph of the line x = 3 passes through the point

The graph of the line y = 2 passes through the point

The graph of the line y = –3 does not pass through the point

A linear equation in two variables x and y is of the form ax + by + c = 0, where

Any point on x-axis is of the form:

Any point on y-axis is of the form:

How many linear equations in x and y can be satisfied by x = 2, y = 3?

The graph of the linear equation 3x + 2y = 6 is the line which meets the x-axis at the point

The graph of the linear equation 2x + 5y = 10 is the line which meets the y-axis at the point

If each of ( – 2, 2), (0, 0) and (2, – 2) is a solution of a linear equation in x and y, then the equation is

The graph of the linear equation x – y = 0 passes through the point

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Match the following columns:

Write each of the following in the form ax + by + c = 0:

(i) x = – 2 (ii) y = 6

Write each of the following in the form ax + by + c = 0:

(i) 3x = 5 (ii) 5y = 4

The total runs scored by two batsmen in a one – day cricket match is 215. Express this information in the form of a linear equation in two variables.

The weight of a book is three times the weight of a note book. Express this fact in the form of an equation in two variables.

Check which of the following are solutions of the equation 2x – 3y = 6.

(i) (3, 0) (ii) (0, 2)

(iii) (2, 6) (iv) (6, 2)

Find the value of k, if x = 3, y = 1 is a solution of the equation 2x + 5y = k.

Find four different solutions of 2x + y = 6.

Express y in terms of x, given that Check whether ( – 5, 2) is a solution of the given equation.

Show that (3, 1) as well as (2, – 2) are the solutions of the equation 3x – y = 8. Find two more solutions. How many solutions can we find?

For the equation 6x – 5y = 8, verify that

(i) (3, 2) is a solution (ii) (2, 3) is not a solution

If the point (3, 4) lies on the graph of the equation 3y = ax + 7, find the value of a.

Find two solutions for each of the following:

(i) 3x + 4y = 12 (ii) 3x + 5y = 0

(iii) 4y + 5 = 0

Study the graph given below. Choose the equation whose graph is given:

(i) y = x (ii) y = 2x

(iii) y = 2x + 1 (iv) x + y = 0

Draw the graph of the equation 3x + 5y – 15 = 0 and show that x = 1, y = 2 is not a solution of the given equation.

Draw the graph of the equation 3x + 2y = 12. At what points does the graph cut the x-axis and the y-axis?

Draw the graph of the equation x – 2y = 6. Verify that each of the points P(2, – 2), Q(4, – 1), and R( – 2, – 4) lies on the straight line.

There are two scales of measuring temperature, namely, Fahrenheit (F) and Celsius (C).

The relation between the two scales is given by

(i) Draw the graph of the given linear equation taking C along x-axis and F along y-axis.

Fill in the blanks given below:

(ii) 0°C = (…)°F (iii) 95°F = (…)°C

(iv) 0°F = (…)°C

(v) Find the temperature which is numerically the same in both (F) and (C).

A taxi charges Rs 20 for the first km and @ Rs 12 per km for subsequent distance covered. Taking the distance covered as x km and total fare Rs y, write a linear equation depicting the relation in x and y.

Draw the graph between x and y.

From your graph find the taxi charges for covering 16 km.

Ans. y = 12x + 8, Rs 200

If the work done by a body on applying a constant force is directly proportional to the distance travelled by the body, then express this in the form of an equation in two variables by taking the constant force as 4 units. From the graph, find the work done when the distance travelled is (i) 2 units (ii) 0 units (iii) 5 units.

For the equation 5x + 8y = 50, if y = 10, then the value of x is

The linear equation 2x + 5y = 16 has

Express in the form ax + by + c = 0.

If 5y – 3x + 15 = 0, then express y in terms of x.

For what value of k does the point (k, – 3) lies on the line 3x – y = 6?

If x = 3, y = – 2 satisfies 2x – 3y = k, then find the value of k.

Find the points where the graph of the equation 3x + 4y = 12 cuts the x-axis and the y-axis.

The area of the triangle formed by the line x + 3y = 12 and the coordinate axes is

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

The question consists of two statements, namely, Assertion (A) and Reason (R). Choose the correct option.

Match the following columns:

The correct answer is:

(a) – ……., (b) – ……., (c) – ……., (d) – …….,

Give the geometrical representation of x = 3 as an equation in

(i) one variable (ii) in two variables

For the line 2x + 3y = 6, we have

(i) x – intercept = ……. (ii) y – intercept = …….

Draw the graph of the line y = x and show that the point (2, 3) does not lie on it.

Draw the graph of 2x – 3y = 4. From the graph, find whether x = – 1, y = – 2 is a solution or not.

The runs scored by two batsmen in a cricket match are 164. Write a linear equation in two variables x and y. Also write a solution of this equation.

Find whether the given statement is true or false:

(i) x = 2, y = 3 is a solution of the equation 5x – 3y = 1.

(ii) y = 2x + 5 is a straight line passing through the point (1, 5).

(iii) The area bounded by the line x + y = 6, the x-axis and the y-axis is 18 sq units.

Two men start from points A and B respectively, 42 km apart. One walks from A to B at 4 km/hr and another walks from B to A at a certain uniform speed. They meet each other after 6 hours. Find the speed of the second man.

The taxi fare in a city is such that Rs 50 is the fixed amount and Rs 16 per km is charged. Taking the distance covered as x km and total fare as Rs y, write a linear equation in x and y. What is the total fare for 20 km?

Draw the graph for each of the equations x + y = 6 and x – y = 2 on the same graph paper and find the coordinates of the point where the two straight lines intersect.