Graphical Solution
ICSE · Class 9 · Mathematics
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What is the y-intercept of the linear equation 2x + 3y = 12?
Find the x-intercept of the line x - 2y = 8.
What is the slope of the line passing through points (2, 3) and (4, 7)?
If two lines 2x + y = 5 and x - y = 1 intersect at point P, what are the coordinates of P?
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Which of the following points lie on the line y = 2x + 1? (Select all correct answers)
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(0, 1), (1, 3), (2, 5), (-1, -1)
Substitute each point into y = 2x + 1: (0,1): 1 = 2(0) + 1 = 1 ✓; (1,3): 3 = 2(1) + 1 = 3 ✓; (2,5): 5 = 2(2) + 1 = 5 ✓; (3,6): 6 = 2(3) + 1 = 7 ✗; (-1,-1): -1 = 2(-1) + 1 = -1 ✓
Which of the following are characteristics of the line x + y = 0? (Select all correct answers)
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Passes through origin, Has slope -1, x-intercept is 0, Passes through (1, -1)
Rewriting x + y = 0 as y = -x: passes through (0,0), slope is -1, both intercepts are 0, and point (1,-1) satisfies the equation: 1 + (-1) = 0 ✓
A line passes through points (0, 2) and (3, 8). What is its equation?
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y = 2x + 2
Slope m = (8-2)/(3-0) = 6/3 = 2. Using point-slope form with (0,2): y - 2 = 2(x - 0), so y = 2x + 2.
What is the solution to the system: 3x + y = 7 and x - y = 1?
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x = 2, y = 1
Adding the equations: (3x + y) + (x - y) = 7 + 1, gives 4x = 8, so x = 2. Substituting in x - y = 1: 2 - y = 1, so y = 1.
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