THE INCLINATION OF THE LINE Y-√3 X -5=0
2 points
30°
90°
60°
45°
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Answers
Answer:
Determine the equation of the straight line whose gradient is and which intersects the y-axis at a distance of 4 units from the origin.
2. Find the value of k, given that the line y2 = 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 x-axis and intersects the x-axis at a distance of (-3) units from the origin.
4. If the line y2 = 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 x-axis 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 co-ordinates 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. (35, 210)
7. x + 6y + 4 = 0
8. k = 45
9. (- 4, - 8)
10. 3x + 2y = 12 or x + y = 5
11. x + y - 2 = 0 and x - y + 1 = 0
Step-by-step explanation:
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The correct answer is 60°.
The angle formed by a line with the positive x-axis is known as a line's inclination. We must first write the equation in slope-intercept form (y = mx + b), where m is the line's slope, in order to get the inclination of the line y - 3 x - 5 = 0.
By rearranging the equation provided, we obtain:
y = √3 x + 5
We can observe that the slope of the line is 3 by comparing this equation to y = mx + b.
The slope of the line determines the tangent of the angle formed by the line with the positive x-axis. As a result, the inclination angle's tangent is 3.
A 60° angle has a tangent of 3. Hence, the line y - 3 x - 5 = 0 has a 60° inclination.
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