Point Slope Form of a Straight Line

Q.

The equation of the horizontal line passing through the point $(4,-7)$ is:

1. $y-7=0$

2. $y-4=0$

3. $y+7=0$

4. $y+4=0$

Q. Given the linear equation x - 2y - 6 = 0, write another linear equation in these two variables, such that the geometrical representation of the pair so formed is:
(i) coincident lines (ii) intersection lines

Q.

Write down the equation of the line whose gradient is $\frac{3}{2}$ and which passes through P, where P divides the line segment joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

Q.

For the straight lines given by the equation $(2+k)x+(1+k)y=5+7k,$ for different values of k which of the following statements is true

1. Lines are parallel

2. Lines pass through the point $(–2,9)$

3. Lines pass through the point $(2,–9)$

4. None of these

Q.

Find the equation of the line passing through (- 2, 3) with slope - 4.

1. 2x + y + 5 = 0

2. 4x + y + 1 = 0

3. 4x - y + 5 = 0

4. 4x +y + 5 = 0

Q.

The equation of the line passing through origin with slope = 1 is:

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

Q.

Find the equation of a line whose $x$ intercept is 8 and passing through the point (4, -8).

1. $y=7x+35$

2. $y=2x-16$

3. $y=2x+16$

4. $y=7x+30$

Q.

Find the equations of the lines passing through point (-2, 0) and equally inclined to the co-ordinate axes.

Q. Half the perimeter of a rectangular garden is 36 m . If the length is 4 m more than its width , find the dimension of garden.

Q.

The equation of a line is 3x +4y -7 = 0. Find the slope of the line.

Q.

Aju was standing at the corner of a square field. He started walking towards North-East direction. When he was $10\sqrt{2}$ m away from where he started, he took a left turn and started walking again. Considering the square field as the coordinate plane and starting point as the origin, find the equation of Aju’s current path.

1. x + y + 20 = 0

2. x + y – 20 = 0

3. x – y = 0

4. x + y = 0

Q.

The equation of a straight line passing through the origin and perpendicular to the straight line 2x +3y -7 = 0 is

1. 3y +2x = 0

2. 2y +3x = 0

3. 2y - 3x = 0

4. None of these

Q. Which of the following is the equation of a line passing through origin with slope equal to 1?

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

Q.

Equation of the straight line whose slope is 3 and passing through the point of intersection of the lines 3x + 4y = 7 and
x − y + 2 = 0 is ____.

1. $21x-7y+16=0$

2. $9x-3y+14=0$

3. $21x-7y+12=0$

4. $9x-3y+5=0$

Q.

Equation of the straight line whose slope is 3 and passing through the point of intersection of the lines 3x + 4y = 7 and
x − y + 2 = 0 is ____.

1. $21x-7y+16=0$

2. $9x-3y+14=0$

3. $21x-7y+12=0$

4. $9x-3y+5=0$

Q.

The equation of the line through origin with slope = 1

1. $5x+4y=0$

2. $3x+4y=2$

3. $x–y=0$

4. $x+y=0$

Q.

Equation of the line passing through (1, 2) and parallel to the line

$y=3x–1$ is

1. y + 2 = x + 1
2. y + 2 = 3(x + 1)
3. y – 2 = 3(x – 1)
4. y – 2 = x – 1

Q. The pair of equations: 4x + 8y = 80 and 4x + 8y = 180 are :

1. parallel
2. intersecting
3. coincident
4. paarllel to x-axis

Q. If for a function $f\left(x\right),f^{\prime }\left(c\right)>0$ then at $x=c$, $f$ is

1. monotonic decreasing
2. monotonic increasing
3. not necessarily monotonic
4. cosntant

Q. Show graphically that the system of equations $2x+3y=4,4x+6y=12$ is inconsistent.

Q.

Find the equation of the line passing through the intersection of $2x+y=8,3x–7=y$ and parallel to $4x+y=11$.

1. $4x+y=14$

2. $x+4y-10=0$

3. $3x+4y-14=0$

4. $3x+y-11=0$

Q.

AB & CD are lines with equations 2 – y + 2 = 0 & – 2y = 2 respectively, where

A & C are y – intercepts & B & D are – intercepts of the respective lines.

1. A(0 , 1); B(-2 , 0);C(0 , -2); D(1 , 0); ¼

2. A(0 , 2); B(-1 , 0);C(0 , -1); D(2 , 0); ¼

3. A(0 , -2); B(1 , 0);C(0 , 1); D(-2 , 0); ½

4. A(0 , 2); B(-1 , 0);C(0 , -1); D(2 , 0); ½

5. A(0 , 4); B(-2 , 0);C(0 , -2); D(4 , 0); 1

Q. Solve the following pair of equations by method of substitution:

Q. One vertex of an equilateral triangle is $(2,3)$ and the equation of one side is $x-y+5=0$, then the equations to the other sides are

1. $y-3=-(2\pm \sqrt{3})(x-2)$
2. $y-3=(\sqrt{3}\pm 1)(x-2)$
3. $y-3=(\sqrt{2}\pm 1)(x-2)$
4. $y-3=(\sqrt{5}\pm 1)(x-2)$

Q. The vertex of the curve obtained by plotting $y=-3x^2$ is ___ .

1. {1, 0}
2. Cannot be determined
3. {0, 0}
4. {0, 1}

Q. The equation of the following line in double intercept form, the $x-$intercept and the $y-$intercept are respectively.

1. $\frac{x}{2}-\frac{y}{2}=1,$ $a=2,b=-2$
2. $-\frac{x}{2}+\frac{y}{2}=1$, $a=2,b=-2$
3. $\frac{x}{2}+\frac{y}{2}=1,$ $a=2,b=2$
4. $\frac{x}{2}-\frac{y}{2}=1,a=-2,a=2$

Q. Write the following equations of lines in slope intercept form.
(i) 2y $-$ 3x + 5 = 0

Q. Find the equation of a line, which has the y intercept 4, and is parallel to the line $2x-3y=7$. Find the co-ordinates of the point, where it cuts the x-axis.

1. $(6,0)$
2. $(-6,0)$
3. $(-8,0)$
4. None of these

Q. Find the equation of a straight line passing through the origin and perpendicular to the straight line 2x + 3y - 7 = 0.

Q. Find the slope of the line passing through the following pairs:

1. $-\frac{\sqrt{3}}{3}$
2. $\frac{3}{\sqrt{3}}$
3. $-\frac{3}{\sqrt{3}}$
4. $\frac{\sqrt{3}}{3}$