FINDING THE EQUATION OF A STRAIGHT LINE WORKSHEET

1) Write the equations of the straight lines parallel to x- axis which are at a distance of 5 units from the x-axis.

Solution

2) Find the equations of the straight lines parallel to the coordinate axes and passing through the point (-5, -2).

Solution

3) Find the equation of a straight line whose

(i) slope is -3 and y-intercept is 4. 

(ii) angle of inclination is 60° and y-intercept is 3. 

Solution

4) Find the equation of the line intersecting the y- axis at a distance of 3 units above the origin and tanθ = 1/2, where θ is the angle of inclination. Solution

5) Find the slope and y-intercept of the line whose equation is 

(i) y = x + 1 

(ii) 5x = 3y 

(iii) 4x - 2y + 1 = 0   

(iv) 10x + 15y + 6 = 0 Solution

6) Find the equation of the straight line whose

(i) slope is -4 and passing through (1, 2)

(ii) slope is 2/3 and passing through (5, -4)

Solution

7) Find the equation of the straight line which passes through the midpoint of the line segment joining (4, 2) and (3, 1) whose angle of inclination is 30°. Solution

8) Find the equation of the straight line passing through the points

(i) (-2, 5) and (3, 6) (ii) (0, -6) and (-8, 2) Solution

9) Find the equation of the median from the vertex R in a Δ PQR with vertices at P(1, -3), Q(-2, 5) and R(-3, 4).

Solution

10) By using the concept of the equation of the straight line, prove that the given three points are collinear.

(i) (4, 2), (7, 5) and (9, 7) (ii) (1, 4), (3, -2) and (-3, 16)

Solution

11) Find the equation of the straight line whose x and y-intercepts on the axes are given by 

(i) 2 and 3

(ii) -1/3 and 3/2

(iii) 2/5 and -3/4 Solution

12) Find the x and y intercepts of the straight line

(i) 5x + 3y - 15 = 0 (ii) 2x - y + 16 = 0 (iii) 3x + 10y + 4 = 0

Solution

13) Find the equation of the straight line passing through the point (3, 4) and has intercepts which are in the ratio 3 : 2. Solution

14) Find the equation of the straight lines passing through the point (2, 2) and the sum of the intercepts is 9. Solution

15) Find the equation of the straight line passing through the point (5, -3) and whose intercepts on the axes are equal in magnitude but opposite in sign. Solution

16) Find the equation of the line passing through the point (9, -1) and having its x-intercept thrice as its y-intercept. Solution

17) A straight line cuts the coordinate axes at A and B. If the midpoint of AB is (3, 2), then find the equation of AB. Solution   

18) Find the equation of the line passing through (22, -6) and having intercept on x-axis exceeds the intercept on y-axis by 5. Solution

19) If A(3, 6) and C(-1, 2) are two vertices of a rhombus ABCD, then find the equation of straight line that lies along the diagonal BD. Solution

20) Find the equation of the line whose gradient is 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 internally. Solution

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