Standard Equation of a Straight Line

Q.

Derive the expression for slope of a line $y=mx+c$

Q.

Which of the following points lie on the line x + y = 3

1. (1, 3)

2. (0, 2)

3. (2, 1)
4. (2, 2)

Q. The slope of the line whose inclination is ${60}^0$ is

1. \N
2. 1
3. $\sqrt{3}$

Q.

Find the equation of a line with slope (m) = -3 and y - intercept (c) = -2.

1. y=-3x+2

2. y=3x-2

3. y=3x+2

4. y=-3x-2

Q.

Find the equation of straight line which passes through the point (3, 4) and sum of its intercepts on the x and y axis is 14

1. x + y = 7

2. 4x + 3y = 24

3. x + y = 14

4. 3x + 4y = 24

Q.

The equation of the straight line which passes through the point (3, 4) and whose intercept on y-axis is twice that on x-axis, is

1. 2x + y = 10

2. None of these

3. 2x – y = 10

4. x + 2y = 10

Q.

Find the slope (m) and y - intercept (c) of the line y = -x.

1. m = -1, c = -1

2. m = -1, c = 1

3. m = 0, c = -1

4. m = -1, c = 0

Q.

The inclination of the line root3x-y+3=0 with the positive X-axis is

Q.

Find the slope (m) and y - intercept (c) of the line $y=4x-\frac{1}{2}$.

1. $m=4,c=-1$

2. $m=4,c=\frac{1}{2}$

3. $m=4,c=-\frac{1}{2}$

4. $m=4,c=2$

Q. Find the sum of the x-coordinates of the intersection of x^2 + y^2 = 36 and x^2 - y^2 = 6.

Q. Write the values of a, b and c for the equation when written in the standard form where $ax+by+c=0:$
$y=0.5x+\sqrt{7}.$

1. $0.5,1,\sqrt{7}$
2. $0.5,1,-\sqrt{7}$
3. $0.5,-1,\sqrt{7}$
4. $-0.5,1,\sqrt{7}$

Q.

If the point P(3, a) lies on the line x + 2y = 3, then find the value of a.

1. 2

2. 1

3. 0

4. -1

Q. What are the values of a, b and c for the equation $y=0.5x+\sqrt{7}$ when written in the standard form: $ax+by+c=0$ ?

1. $0.5,1,\sqrt{7}$
2. $0.5,1,-\sqrt{7}$
3. $-0.5,1,-\sqrt{7}$
4. $0.5,1,-\sqrt{7}$

Q.

List-II gives distance between pair of points given in List-I. Match them correctly.
$\begin{array}{cccc}& List-I& & ListII\\ \left(P\right)& (-5,7),(-1,3)& \left(1\right)& 5\\ \left(Q\right)& (5,6),(1,3)& \left(2\right)& \sqrt{8}\\ \left(R\right)& (\sqrt{3}+1,1),(0,\sqrt{3})& \left(3\right)& \sqrt{6}\\ \left(S\right)& (0,0),(-\sqrt{3},\sqrt{3})& \left(4\right)& 4\sqrt{2}\end{array}$

1. P-3, Q-2, R-4, S-1

2. P-4, Q-3, R-2, S-1

3. P-4, Q-1, R-2, S-3

4. P-1, Q-2, R-3, S-4

Q. Write the values of a, b and c for the equation $y=0.5x+\sqrt{7}$
when written in the standard form where $ax+by+c=0:$

1. $0.5,1,-\sqrt{7}$
2. $0.5,-1,\sqrt{7}$
3. $-0.5,1,\sqrt{7}$
4. $0.5,1,\sqrt{7}$

Q.

Can anyone explain this question give the equation of a line passing through the point (3, 5)

Q.

Find the equation of straight line which passes through the point (3, 4) and sum of its intercepts on the x and y axis is 14

1. x + y = 7

2. 4x + 3y = 24

3. x + y = 14

4. 3x + 4y = 24

Q. What are the values of a, b and c for the equation when written in the standard form: $ax+by+c=0:$
$y=0.5x+\sqrt{7}.$

1. $0.5,1,\sqrt{7}$
2. $0.5,1,-\sqrt{7}$
3. $0.5,-1,\sqrt{7}$
4. $-0.5,1,\sqrt{7}$

Q. The inclination of the line whose slope is zero is

1. $0^0$
2. ${30}^0$
3. ${60}^0$

Q. M (-2, y) is a point equidistant from the points A(5, 7) and B(3, -4). Find the value of y.

Q.

Find the slope of a line whose Y intercept is 3 and which passes through (4, 11)

__

Q. The equation of the line though origin with slope = 1

1. 5x + 4y = 0
2. 3x + 4y = 2
3. 4x – 5y = 0
4. 5x – 4y = 0

Q.

The x and y intercepts of the line x + y = 3 are:

1. 

2. 

3. 

4. 

Q.

The x and y intercepts of the line x + y = 3 are:

1. 1 and 1

2. 0 and 0

3. ^1/₃ and ¹/₃

4. 3 and 3

Q. From the choices given below, choose the equation whose graph is given below:

Fig. \( 4.7 \)

1. $y=x-2$
2. $y=x+2$
3. $x+2y=6$
4. $y=-x+2$

Q. Write the values of $a$, $b$ and $c$ for the equation when written in the standard form where $ax+by+c=0:$
$y=0.5x+\sqrt{7}.$

1. $0.5,1,\sqrt{7}$
2. $0.5,1,-\sqrt{7}$
3. $0.5,-1,\sqrt{7}$
4. $-0.5,1,\sqrt{7}$

Q. Write the equation in standard form $4x^2+5=\sqrt{3}x$

1. $x^2-3\sqrt{z}=0$
2. $4x^2-\sqrt{3}x+5=0$
3. $4x^2-3\sqrt{z}=0$
   
4. $4x^2+\sqrt{3}z+5=0$

Q.

The co-ordinate of the point which divides the line joining the points (–1, 7) and (4, –3) in the ratio 2:3 is ________.

1. (1, 3)

2. (-1, 3)

3. (-1, -3)

4. (1, -3)

Q.

If the point P(3, a) lies on the line x + 2y = 3, then find the value of a.

1. 2

2. 1

3. 0

4. -1

Q. Pair the cards with ordered pair $(x,y)$ for the equation $y=2x+1$

1. $x=1$
2. $y=3$
3. $x=0$
4. $y=1$
5. $x=-1$
6. $y=-1$
7. $x=-2$
8. $y=-3$