Practice the questions given in the worksheet on equation of a straight line.
1. Determine the equation of the straight line whose gradient is and which intersects the yaxis at a distance of 4 units from the origin.
2. Find the value of k, given that the line \(\frac{y}{2}\) = x – k passes through the point (4, 4)
3. Find the equation of the straight line which makes an angle 450 with the positive direction of xaxis and intersects the xaxis at a distance of (3) units from the origin.
4. If the line \(\frac{y}{2}\) = 3x  6 passes through the point (p, 2p), find the value of p.
5. Determine the equation of the straight line whose inclination is 60° and which passes through the point (3, 4).
6. Find the point midway between the point (1, 3) and the point intersection of the lines 4x + y  10= 0 and 2x + 3y  8 = 0.
7. Find the equation of the straight line which cuts off an intercept ( 4) from the xaxis and passes through the point (2,  1).
8. If the slope of the line joining the points (2k,  2) and (1,  k) be ( 2), find k.
9. Find the coordinates of the point on the line 7x  6y = 20 for which the ordinate is double the abscissa.
10. A straight line passes through the point (2, 3) and is such that the sum of its intercepts on the coordinate axes is 10. Find the equation of the straight line.
11. Prove that the line lines x  2 = 0, x + 1 = 0, y = 0 and y  3 = 0 form a square. Find the equations of its diagonals.
Answers for the worksheet on on equation of a straight line are given below:
Answers:
1. 3x + 2y = 8
2. k = 6
3. x  y + 3 = 0
4. p = 3
5. y  4 = √3(x  3)
6. (\(\frac{3}{5}\), \(\frac{21}{0}\))
7. x + 6y + 4 = 0
8. k = \(\frac{4}{5}\)
9. ( 4,  8)
10. 3x + 2y = 12 or x + y = 5
11. x + y  2 = 0 and x  y + 1 = 0
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