Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ Question 14: Find equation of the line through the points (0, 2) making an angle 2 with the positive x-axis. 3 Also, find the equation of the line parallel to it and crossing the y-axis at a distance of 2 units below the origin. Solution 14: The slope of the line making an angle 2 with the positive x-axis is m = tan 2 3 3 3 Now, the equation of the line passing through points (0, 2) and having a slope 3 is y2 3( x0) i. e., 3x y 2 0 The slope of line parallel to line 3x y2 0 is 3 . It is given that the line parallel to line 3x y2 0 crosses the y-axis 2 units below the origin i.e., it passes through point (0, 2). Hence, the equation of the line passing through points (0, 2) and having a slope 3 is y 2 3 x0 y 2 3x 3x y 2 0 Question 15: The perpendicular from the origin to a line meets it at the point (-2, 9), find the equation of the line. Solution 15: 90 9 The slope of the line joining the origin (0, 0) and point (-2, 9) is m1 2 0 2 Accordingly, the slope of the line perpendicular to the line joining the origin and points (-2, 9) is 1 1 2 m2 m 9 1 9 2 Now, the equation of the line passing through point (-2, 9) and having a slope m2 is 2 ( y9) x 2 9 9y81 2x 4 i.e., 2x-9y+85=0 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 10 – Straight Lines Maths ______________________________________________________________________________ Question 16: The length L (in centimeter) of a copper rod is a linear function of its Celsius temperature C. In an experiment, if L = 124.942 when C = 20 and L = 125.134 when C = **11**0, express L in terms of C. Solution 16: It is given that when C = 20, the value of L is 124.942, whereas when C = **11**0, the value of L is 125.134. Accordingly, points (20, 124.942) and (**11**0, 125.134) satisfy the linear relation between L and C. Now, assuming C along the x-axis and L along the y-axis, we have two points i.e., (20, 124.942) and (**11**0, 125.134) in the XY plane. Therefore, the linear relation between L and C is the equation of the line passing through points (20, 124.942) and (**11**0, 125.134). 125.134 124.942 L-124.942 C 20 **11**0 20 0.192 L-124.942 C 20 90 0.192 i. e., L= C 20 124.942. which is required linear relation. 90 Question 17: The owner of a milk store finds that, he can sell 980 liters of milk each week at Rs. 14/liter and 1220 liters of milk each week at Rs. 16/liter. Assuming a linear relationship between selling price and demand, how many liters could he sell weekly at Rs. 17/liter? Solution 17: The relationship between selling price and demand is linear. Assuming selling price per liter along the x-axis and demand along the y-axis, we have two points i.e., (14, 980) and (16, 1220) in the XY plane that satisfy the linear relationship between selling price and demand. Therefore, the line passing through points (14, 980) and (16, 1220). 1220 980 y980 x14 16 14 240 y980 x14 2 y980 120 x14 i.e., y=120 x-14 980 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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