# Slope of a Line

## Trending Questions

**Q.**

If two lines are perpendicular, then the product of their slope is _____.

0

1

-1

infinite

**Q.**In which ratio is the line segment joining points (-3, -4) and (1, -2) divided by y - axis

**Q.**Draw the graph of the lines x = $-$2 and y = 3 . Write the vertices of the figure formed by these lines , the x-axis and the y-axis . Also , find the area of the figure.

**Q.**Draw the graphs of the following equations on the same graph paper:

$2x+y=2\phantom{\rule{0ex}{0ex}}2x+y=6$

Find the coordinates of the vertices of the trapezium formed by these lines. Also, find the area of the trapezium so formed.

**Q.**The product of slopes of two perpendicular lines is

**Q.**

Find the slope, x-intercept & y-intercept of the straight line 2x - 3y + 5 = 0.

**Q.**The line segment joining the points P(3, 3) and Q(6, −6) is trisected at the points A and B such that A is nearer to P. If A also lies on the line given by 2x + y + k = 0, find the value of k.

**Q.**

A (1, 4), B (3, 2) and C (7, 5) are vertices of a triangle ABC. Find :

(i) the co-ordinates of the centroid of triangle ABC.

(ii) the equation of a line, through the centroid and parallel to AB.

**Q.**Show that the points A (1, −2), B (3, 6), C (5, 10) and D (3, 2) are the vertices of a parallelogram.

**Q.**What is wavy curve method .? What are the steps to solve inequality by wavy curve method?

**Q.**What is the slope of a line segment whose inclination is 135∘?

- 1
- -1
- 2
- -2

**Q.**

The line joining P(−4, 5) and Q(3, 2) intersect the y-axis at point R .PM and QN are perpendicular to P and Q on the x- axis. Find:

(1) the ratio PR:RQ.

(2) the coordinate of R.

(3) the area of the quadrilateral PMNQ.

**Q.**

Find the slope, x-intercept & y-intercept of the straight line 2x - 3y + 5 = 0.

**Q.**

The number of integral values of $m$ so that the abscissa of point of intersection of lines $3x+4y=9$ and $y=mx+1$ is also an integer, is:

$3$

$2$

$1$

$0$

**Q.**

In fig., OP is equal to diameter of the circle. Prove that ΔABP is an equilateral triangle.

**Q.**Find the slope of the line passing through the points A(4, -1) and B(-3, 5).

- −76
- −67
- 67
- 76

**Q.**

If a line passes through the point (1, 2) and cuts off positive intercepts on the x–axis and y–axis in the ratio 2 : 3, find the equation of the line.

7 = 3x + 2y

5= 3x + 8y

4 = 3x + 2y

3 = 2x + 7y

**Q.**

A line through the point $A(2,0)$ which makes an angle of $30\xb0$with the positive direction of X-axis is rotated about$A$ in clockwise direction through an angle of $15\xb0$ . Then, the equation of the straight line in the new position is

$(2\u2013\sqrt{3})x+y+4-2\sqrt{3}=0$

$(2\u2013\sqrt{3})x\u2013y\u20134+2\sqrt{3}=0$

$(2\u2013\sqrt{3})x+y-4-2\sqrt{3}=0$

$(2\u2013\sqrt{3})x+y+4+2\sqrt{3}=0$

**Q.**

Inclination of a line parallel to x axis is _____.

0 degree

90 degree

80 degree

40 degree

**Q.**What is a slope?

**Q.**

The co-ordinates of two points P and Q are (2, 6) and (-3, 5) respectively. Find :

(i) the gradient of PQ;

(ii) the equation of PQ;

(iii) the co-ordinates of the point where PQ intersects the x-axis.

**Q.**

The line joining the points $(-1,3)$and $(4,-2)$ will pass through the point $(p,q)$if

$p\u2013q=1$

$p+q=1$

$p\u2013q=2$

$p+q=2$

**Q.**If (−2, 1) is the centroid of the triangle having its vertices at (x , 0) (5, −2), (−8, y), then x, y satisfy the relation

(a) 3x + 8y = 0

(b) 3x − 8y = 0

(c) 8x + 3y = 0

(d) 8x = 3y

**Q.**Determine whether the given points are collinear.

(1) A(0, 2), B(1, –0.5), C(2, –3)

(2) $\mathrm{P}\left(1,2\right),\mathrm{Q}\left(2,\frac{8}{5}\right),\mathrm{R}\left(3,\frac{6}{5}\right)$

(3) L(1, 2), M(5, 3) , N(8, 6)

**Q.**

A and B are two points on the x-axis and y-axis respectively. P(2, -3) is the mid point of AB. Find the

(i) co-ordinates of A and B

(ii) slope of line AB

(iii) equation of line AB.

**Q.**The line joining the points (2, 1) and (5, −8) is trisected at the points P and Q. If point P lies on the line 2x − y + k = 0. Find the value of k.

**Q.**

Find the equation of the line whose slope is −56 and x-intercept is 6.

**Q.**If the slope of the line joining the points P(k, 0) and Q(-3, -2) is 27, then k = ______________.

- 1
- 2
- 3
- 4

**Q.**Solve the following system of equations graphically and find the vertices and area of the triangle formed by these lines and the

*y*-axis.

$2x-5y+4=0\phantom{\rule{0ex}{0ex}}2x+y-8=0$

**Q.**

The side AB square ABCD is parallel to the x-axis. Find the slopes of all its sides.

Also, find :

(i) the slope of the diagonal AC,

(ii) the slope of the diagonal BD.