Moderate Level Worksheet
Very Short Answer Questions (1 Mark Each)
(1) Write the equation of a line whose slope is 2 and y-intercept is 3.
Perfect! Using slope-intercept form y = mx + c, where m = 2 and c = 3.
(2) If 2x + 3y = 6, find the y-intercept. y-intercept =
Correct! When x = 0, we get 3y = 6, so y = 2.
(3) Find the value of k if the equation 3x + ky = 9 passes through the point (2, 1). k =
Excellent! Substituting (2, 1): 3(2) + k(1) = 9, so 6 + k = 9, hence k = 3.
(4) Write the coordinates of the point where the line x = 4 meets the y-axis.
Correct! The line x = 4 is parallel to the y-axis and never meets it.
(5) Write the equation of the line parallel to y = 2x + 5 passing through (0, –3).
Perfect! Parallel lines have the same slope (2), and passing through (0, -3) gives y-intercept = -3.
Short Answer Questions (2 Marks Each)
Note: Answer each question with steps and explanation in 2-3 sentences. Write down the answers on sheet and submit to the school subject teacher.
(1) Draw the graph of x + y = 6 using the intercept method. x-intercept (when y = 0):
Excellent! Plot points (6, 0) and (0, 6), then draw the line through them.
(2) Find the point of intersection of the lines 2x + y = 7 and x - y = 1 by graphical method. Point of intersection: x =
Great! The lines intersect at approximately (8/3, 1/3) or (2.67, 0.33).
(3) If 4x - 3y = 12, find the slope of the line. Slope =
Perfect! Converting to y = mx + c form gives slope m = 4/3.
(4) Determine whether the points (2, 3), (4, 7), and (6, 11) are collinear. The points are
Slope between (2,3) and (4,7):
Slope between (4,7) and (6,11):
Correct! Equal slopes confirm the points lie on the same straight line.
(5) Write the equation of the line which passes through (2, 3) and (4, 7).
Slope =
Excellent! Using y -
Long Answer Questions (4 Marks Each)
Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.
(1) The sum of two numbers is 27 and their difference is 5. Form a pair of linear equations and find the numbers graphically. The two numbers are
Perfect! The two numbers are 16 and 11.
(2) A boat goes 16 km downstream in 2 hours, and returns upstream in 4 hours. Find the speed of the boat in still water and the speed of the stream using linear equations. Boat Speed =
Excellent! Boat speed = 6
(3) The sum of the digits of a two-digit number is 9. If 9 is added to the number, the digits interchange their places. Find the number. The number is
Perfect! The two-digit number is 45.
(4) The ratio of the incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each saves ₹2000 per month, find their monthly incomes using the method of linear equations. Monthly incomes: ₹
Excellent! The monthly incomes are ₹9000 and ₹7000.
(5) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Ramesh paid ₹27 for a book kept for 7 days, while Suresh paid ₹21 for a book kept for 5 days. Find the fixed charge and the charge per day. Fixed charge = ₹
Perfect! Fixed charge = ₹ 15, additional charge = ₹ 3 per day.
Part B: Objective Questions (1 Mark Each)
Choose the correct answer and write the option (a/b/c/d)
(1) The graph of a linear equation in two variables is always:
(a) A curve (b) A straight line (c) A circle (d) None of these
Correct! Linear equations always produce straight line graphs.
(2) The equation of the x-axis is:
(a) x = 0 (b) y = 0 (c) y = x (d) x + y = 0
Correct! The x-axis has equation y = 0 (all points have y-coordinate 0).
(3) If 2x + 3y = 6, the slope of the line is:
(a)
Correct! Rearranging to y =
(4) The point (0, 5) lies on the:
(a) x-axis (b) y-axis (c) Both axes (d) None of these
Correct! Points with x-coordinate 0 lie on the y-axis.
(5) The solution of the equations x = 2 and y = 3 is:
(a) (2, 3) (b) (3, 2) (c) (0, 0) (d) (2, 0)
Correct! The solution is the point where both conditions are satisfied: (2, 3).
(6) If two lines are parallel, their slopes are:
(a) Equal (b) Negative reciprocals (c) Zero (d) Undefined
Correct! Parallel lines have equal slopes.
(7) Which of the following is the equation of a horizontal line?
(a) x = 4 (b) y = 4 (c) y = x (d) 2x + y = 5
Correct! y = 4 represents a horizontal line (constant y-value).
(8) The point of intersection of the lines x + y = 4 and x - y = 2 is:
(a) (3, 1) (b) (2, 2) (c) (1, 3) (d) (4, 0)
Correct! Adding the equations: 2x = 6, so x = 3, then y = 1.
(9) Which of the following points lies on 3x - 2y = 6?
(a) (2, 0) (b) (0, -3) (c) (4, 3) (d) (1, 2)
Correct! Substituting (2, 0): 3(2) - 2(0) = 6!
(10) The general form of a linear equation in two variables is:
(a) y = mx + c (b) ax + by + c = 0 (c) x + y = 0 (d) ax + b = 0
Correct! The general form is ax + by + c = 0 where a, b are not both zero.
Linear Equations Properties Challenge
Determine whether these statements about linear equations are True or False: