Graphical Representation of a Linear Equation in 2 Variables

Q.

The taxi fare in a city is as follows: For the first kilometer, the fare is Rs. $8$ and for the subsequent distance it is Rs. $5$ per km. Taking the distance covered as $x$ km and total fare as Rs. $y$, write a linear equation for this information, and draw its graph.

Q.

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

Q.

Draw the graph of the equation, 3x + 2y = 6.

Find the coordinates of the point where the graph cuts the y - axis.

Q.

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

(a) (2, -3)

(b) (3, -3)

(c) (0, -3)

(d) (-3, 2)

Q. Question 6
If the work done by a body on application of a constant force is directly proportional to the distance travelled by the body, express this in the form of an equation in two variables and draw the graph of the same by taking the constant force as 5 units. Also, read from the graph the work done when the distance travelled by the body is:
(i) 2 units (ii) 0 unit

Q.

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

(a) (2, 0)

(b) (3, 0)

(c) (0, 2)

(d) (0, 3)

Q.

Draw the graph of the equation, 2x - 3y = 5.

From your graph, find (i) the value of y when x = 4 and (ii) the value of x when y = 3.

Q.

Draw the graph of the line 4x + 3y = 24.

(i) Write the coordinates of the points where this line intersects the x - axis and the y - axis.

(ii) Use this graph to find the area of the triangle formed by the graph line and the coordinate axes.

Q.

The graph x + 3 = 0 is a line

(a) making an intercept - 3 on the x - axis

(b) making an intercept - 3 on the y - axis

(c) parallel to the y - axis at a distance of 3 units to the left of y - axis

(d) parallel to the x - axis at a distance of 3 units below the x - axis

Q.

The graph of x = 4 is a line

(a) making an intercept 4 on the x-axis

(b) making an intercept 4 on the y-axis

(c) parallel to the x-axis at a distance of 4 units from the origin

(d) parallel to the y-axis at a distance of 4 units from the origin

Q.

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

$\left(i\right)6x-3y=12$ $\left(ii\right)-x+4y=8$ $\left(iii\right)2x+y=6$ $\left(iv\right)3x+2y+6=0$

Q. If the number of hours for which a labourer works is x and y are his wages (in rupees) and y = 2x − 1, then draw the graph of work-wages equation. From the graph, find the wages of the labourer if he works for 6 hours.

Q.

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

$\left(i\right)x+y=4$ $\left(ii\right)x-y=2$ $\left(iii\right)-x+y=6$

$\left(iv\right)y=2x$ $\left(v\right)3x+5y=15$ (vi) $\frac{x}{2}-\frac{y}{3}=2$

(vii) $\frac{x-2}{3}=y-3$ $\left(viii\right)2y=-x+1$

Q.

The graph of the line x - y = 0 passes through the point

(a) $\frac{-1}{2},\frac{1}{2}$

(b) $\frac{3}{2},\frac{-3}{2}$

(c) (0, -1)

(d) (1, 1)

Q. The graph of linear equation in two variables always represents

1. Curve and straight line
2. None of these
3. Curve
4. Straight line

Q.

Draw the graph of the equation, 2x + y = 6.

Find the coordinates of the point where the graph cuts the x - axis.

Q.

Two students A and B together contributed Rs. 100 towards the Prime Minister's Relief Fund to help the earthquake victims, Write a linear equation to satisfy the above data and draw its graph.

Q.

Q.

The graph of y + 2 = 0 is a line

(a) making an intercept of - 2 on the x - axis

(b) making an intercept of - 2 on the y - axis

(c) parallel to the x - axis at a distance of 2 units below the x - axis

(d) parallel to the y - axis at a distance of 2 units to the left of y - axis

Q.

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

1. 4

2. 3

3. 1

4. 2

Q.

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

(i) the number line (ii) the Cartesian plane.

Q.

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

1. (2, 0)

2. (2/3, 0)

3. (0, 3)

4. (3, 0)

Q.

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

(a) (0, 3)

(b) (2, 3)

(c) (3, 2)

(d) none of these

Q.

The graph of the linear equation 3x - 2y = 6 cuts the y-axis at the point (0, 3).

1. (0, 3)

2. (2, 0)

Q.

The Equation y = - 5, in two variables can be written in the form of ax + by + c = 0 as

1. 1.x + 0.y -5 = 0

2. .x + 1.y -5 = 0

3. 1.x + 0.y + 5 = 0

4. 0.x + 1.y + 5 = 0

Q.

Does the equation represent a linear or nonlinear function? Explain.

$\mathrm{Y}=\mathrm{x}+5$

Q.

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

$\left(i\right)(0,3)$ $\left(ii\right)(-0,-4)$ $\left(iii\right)(2,-5)$ $\left(i\right)(3,4)$

Q. Question 10
The graph of y = 6 is a line:


A) parallel to x-axis at a distance 6 units from the origin
B) parallel to y-axis at a distance 6 units from the origin
C) making an intercept 6 on the x-axis
D) making an intercept 6 on both axes

Q.

Give the geometric representations of the following equations

(a) on the number line (b) on the Cartesian plane:

$\left(i\right)x=2$ $\left(ii\right)y+3=0$ $\left(iii\right)y=3$ $\left(iv\right)2x+9=0$ $\left(v\right)3x-5=0$

Q. The point Q($-$3, $-$2) lies on a line parallel to the Y-axis. Write the equation of the line and draw its graph.