Express the following linear equations in the form ax+by+c = 0 and indicate the values of a, b and c in each case:

(i) -2x+3y =12

(ii) x- -5 =0

(iii) 2x+3y=

(iv) 3x = -7y

(v) 2x+3 = 0

(vi) y – 5 = 0

(vii) 4=3x

(viii) y=

Write each of the following as an equation in two variables.

(i) 2x= -3

(ii) y = 3

(iii) 5x =

(iv) y = x

The cost of ball pen is Rs. 5 less than half of the cost of fountain pen. Write this statement as a linear equation in two variables.

Write two solutions for each of the following equations:

(i) 3x+4y =7

(ii) x=6y

(iii) x+πy =4

(iv) x-y =4

Write two solutions of the form x = 0, y = a and x=b, y=0 for each of the following equations:

(i) 5x-2y =10

(ii) -4x+3y =12

(iii) 2x+3y =24

Check which of the following are solutions of the equation 2x-y =6 and which are not:

(i) (3,0)

(ii) (0,6)

(iii) (2,-2)

(iv) (,0)

(v) (, -5)

If x = -1, y = 2 is a solution of the equation 3x+4y=k, find the value of k.

Find the value of λ, if x=-λ and y = is a solution of the equation x+4y-7=0.

If x = 2α+1 and y = α-1 is a solution of the equation 2x-3y+5=0, find the value of α.

If x=1 and y=6 is a solution of the equation 8x-ay+a²=0, find the values of a.

Draw the graph of each of the following linear equations in two variables:

(i) x+y=4

(ii) x-y=2

(iii) -x+y=6

(iv) y=2x

(v) 3x+5y=15

(vi) =2

(vii) =y-3

(viii) 2y= -x+1

Give the equations of two lines passing through (3, 12). How many more such lines are there, and why?

A three-wheeler scooter charges Rs. 15 for dirst kilometre and Rs. 8 each for every subsequent kilometre. For a distance of x km, an amount of Rs. y is paid. Write the linear equation representing the above information.

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Aarushi paid Rs. 27 for a book kept for seven days. If fixed charges are Rs. x and per day charges are Rs. y. Write the linear equation representing the above information.

A number is 27 more than the number obtained by reversing its digits. If its unit’s and ten’s digit are x and y respectively, write the linear equation representing the above statement.

The sum of a two digit number and the number obtained by reversing the order of its digits is 121. If units and ten’s digit of the number of x and y respectively, then write the linear equation representing the above statement.

Plot the points (3,5) and (-1,3) on a graph paper and verify that the straight line passing through these points also passes through the point (1,4).

From the choices given below, choose the equation whose graph in Fig. 13.13.

(i) y = x

(ii) x+y=0

(iii) y=2x

(iv) 2+3y=7x

[Hint: Clearly, (-1,1) and (1,-1) satisfy the equation x+y=0]

From the choices given below, choose the equation whose graph is given in Fig. 13.14

(i) y=x+2

(ii) y=x-2

(iii) y=-x+2

(iv) x+2y=6.

[Hint: Clearly, (2,0) and (-1,3) satisfy the equation y=-x+2]

If the point (2,-2) lies on the graph of the linear equation 5x+ky=4, find the value of k.

Draw the graph of the equation 2x+3y=12. From the graph, find the coordinates of the point.

(i) whose y-coordinates is 3.

(ii) whose x-coordinate is -3.

Draw the graph of each of the equations given below. Also, find the coordinates of the points where the graph cuts the coordinate axes:

(i) 6x–3y=12

(ii) -x+4y=8

(iii) 2x+y=6

(iv) 3x+2y+6=0

Draw the graph of the equation 2x+y=6. Shade the region bounded by the graph and the coordinate axes. Also, find the area of the shaded region.

Draw the graph of the equation =1. Also find the area of the triangle formed by the line and the coordinates axes.

Draw the graph of y = |x|.

Draw the graph of y = |x| +2.

Draw the graphs of the following linear equations on the same graph paper.

2x+3y = 12, x – y = 1

Find the coordinates of the vertices of the triangle formed by the two straight lines and the y-axis. Also, find the area of the triangle.

Draw the graphs of the linear equations 4x-3y+4=0 and 4x+3y-20=0. Find the area bounded by these lines and x-axis.

The path of a train A is given by the equation 3x+4y-12=0 and the path of another train B is given by the equation 6x+8y-48=0. Represent this situation graphically.

Ravish tells his daughter Aarushi, “Seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as old as you will be.” If present ages of Aarushi and Ravish are x and y years respectively, represent this situation algebraically as well as graphically.

Aarushi was driving a car with uniform speed of 60 km/h. Draw distance-time graph. From the graph, find the distance travelled by Aarushi on

(i) 2 Hours

(ii) Hour

Give the geometric representations of the following equations

(a) on the number line

(b) on the Cartesian plane:

(i) x=2

(ii) y+3=0

(iii) y=3

(iv) 2x+9=0

(v) 3x-5=0

Give the geometrical representation of 2x+13=0 as an equation in

(i) One variable

(ii) two variables

Solve the equation 3x+2=x-8, and represent the solution on

(i) the number line

(ii) The Cartesian plane.

Write the equation of the line that is parallel to x-axis and passing through the point

(i) (0,3)

(ii) (0,4)

(iii) (2,-5)

(iv) (-4,-3)

Write the equation of the line that is parallel to y-axis and passing through the point

(i) (4,0)

(ii) (-2,0)

(iii) (3,5)

(iv) (-4,-3)

Write the equation representing x-axis.

Write the equation representing y-axis.

Write the equation of a line passing through the point (0,4) and parallel to x-axis.

Write the equation of a line passing through the point (3,5) and parallel to x-axis.

Write the equation of a line parallel to y-axis and passing through the point (-3,-7).

A line passes through the point (-4,6) and is parallel to x-axis. Find its equation.

Solve the equation 3x-2=2x+3 and represent the solution on the number line.

Solve the equation 2y-1 = y+1 and represent it graphically on the coordinate plane.

If the point (a,2) lies on the graph of the linear equation 2x-3y+8=0, find the value of a.

Find the value of k for which the point (1,-2) lies on the graph of the linear equation x-2y+k=0.

If (4,19) is a solution of the equation y=ax+3, then a=

If (a,4) lies on the graph of 3x+y=10, then the value of a is

The graph of the linear equation 2x-y=4 cuts x-axis at

How many linear equations are satisfied by x=2 and y=-3?

The equation x-2=0 on number line is represented by

x=2, y=-1 is a solution of the linear equation

If (2k-1,k) is a solution of the equation 10x-9y=12, then k=

The distance between the graph of the equations x = -3 and x=2 is

The distance between the graphs of the equations y = -1 and y = 3 is

If the graph of the equation 4x+3y=12 cuts the coordinate axes at A and B, then hypotenuse of right triangle AOB is of length