WORKSHEET OF FINDING SLOPE OF THE LINE

Question 1 :

Find the angle of inclination of the straight line whose slope is

(i) 1          (ii) √3            (iii) 0

Solution

Question 2 :

Find the slope of the straight line whose angle of inclination is

(i) 30°       (ii) 60°         (iii) 90°

Solution

Question 3 :

Find the slope of the straight line passing through the points

(i) (3 , -2) and (7 , 2)

(ii) (2 , -4) and origin

(iii) (1 + √3 , 2) and (3 + √3 , 4)

Solution

Question 4  :

Find the angle of inclination of the line passing through the points

(i) (1, 2) and (2 , 3)

(ii) (3 , 3) and (0 , 0)

(iii) (a , b) and (-a , -b) 

Solution

Question 5 :

Show that the given vertices form a right angled triangle and check whether its satisfies Pythagoras theorem

(i) A(1, -4), B(2, -3) and C(4, -7)

(ii) L(0, 5), M(9, 12) and N(3, 14)

Solution

Question 6 :

Show that the given points form a parallelogram :

A(2.5, 3.5) , B(10, -4), C(2.5, -2.5) and D(-5, 5) 

Solution

Question 1 :

The line joining the points A(-2 , 3) and B(a , 5) is parallel to the line joining the points C(0 , 5) and D(-2 , 1). Find the value of a.

Solution

Question 2 :

The line joining the points A(0, 5) and B(4, 2) is perpendicular to the line joining the points C(-1, -2) and D(5, b). Find the value of b.

Solution

Question 3 :

Line m passes through the points (k, 7) and (3, k - 4) in the xy-plane. If the slope of line m is 3, what is the value of k ?

Solution

Question 4 :

In the xy-plane, a line with slope of 1/3 passes through the points (-1, 1) and (5, n). What is the value of n ?

a) 9    b)   4   c)  3   d) 7/3

Solution

Question 5 :

Line p is shown in the xy-plane, and the point with coordinates (5, r) lies on the line p. What is the value of r ?

a) -5/3    b)  -11/6    c)  -11/7    d) -12/7

Solution

Question 6 :

6x + y = 17

hx - 9y = -8

In the given pair of equations, h is  a constant. The graphs of the equations in the xy-plane are perpendicular lines. What is the value of h ?

Solution

Question 7 :

The linear function f is defined by f(x) = ax + b where a  and b are constants. If the graph of y = f(x) in the xy-plane has a slope of 6 and passes through the point (-5, -14). What is the value of b ?

Solution

Question 8 :

A line in the xy-plane, the line with equation ax - (1/3)y = 8, where a is a constant, passes through the point (2, 6). What is the x-coordinate of the x-intercept of the line ?

Solution

Question 1 :

Find the slope of the line which passes through the origin and the midpoint of the line segment joining the points (0 ,- 4) and (8 , 0).

Solution

Question 2 :

The side AB of a square ABCD is parallel to x-axis . Find the

(i) slope of AB (ii) slope of BC (iii) slope of the diagonal AC

Solution

Question 3 :

The side BC of an equilateral Δ ABC is parallel to x-axis. Find the slope of AB and the slope of BC

Solution

Question 4 :

A line in the xy-plane is defined by the equation y = ax + b, where a and b are constants. The line passes through the points (0, -79) and (5, 91). What is the value of a + b ?

Solution

Question 5 :

The table shows three values of x and their corresponding values of y, where p is a constant. There is a linear relationship between x and y. What is the slope of the line that represents this relationship in the xy-plane?

a) -57/4   b)  57/4     c)  -(p - 57)/4     d)  (2p + 57)/4

Solution

Question 6 :

The graph of the equation 5x - 8y = k, where k is a constant, is a line in the xy-plane. The line has an x-intercept at (m , 0) and a y-intercept at (0, n), where m and n are constants. What is the value of m/n ?

a)  -8/5     b)  -5/8    c)  5/8    d)  8/5

Solution

Question 7 :

In the xy-plane, line m has an x-intercept at (a, b + 4), where a and b are constants. If the line m passes through the points (b, -11) and (b + 6, 7), what is the value of a ?

Solution

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