Equation of a Line
ICSE · Class 10 · Mathematics
Flashcards for Equation of a Line — ICSE Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allFind the slope of the line passing through the points (2, 3) and (6, 11).
Answer
Step 1: Use the slope formula: m = (y2 - y1) / (x2 - x1) Step 2: Substitute the points (2, 3) and (6, 11): m = (11 - 3) / (6 - 2) Step 3: Simplify: m = 8 / 4 = 2 Answer: The slope is 2.
Find the slope of the line joining (-4, 5) and (2, -7).
Answer
Step 1: Use m = (y2 - y1) / (x2 - x1) Step 2: Take (x1, y1) = (-4, 5), (x2, y2) = (2, -7) Step 3: m = (-7 - 5) / (2 - (-4)) Step 4: m = -12 / 6 = -2 Answer: The slope is -2.
Find the equation of the line passing through (3, 4) with slope 5.
Answer
Step 1: Use point-slope form: y - y1 = m(x - x1) Step 2: Substitute x1 = 3, y1 = 4, m = 5 Step 3: y - 4 = 5(x - 3) Step 4: Expand: y - 4 = 5x - 15 Step 5: Add 4 to both sides: y = 5x - 11 Answer: y = …
Find the equation of the line through (1, -2) with slope -3.
Answer
Step 1: Use y - y1 = m(x - x1) Step 2: Substitute x1 = 1, y1 = -2, m = -3 Step 3: y - (-2) = -3(x - 1) Step 4: y + 2 = -3x + 3 Step 5: Subtract 2 from both sides: y = -3x + 1 Answer: y = -3x + 1.
Find the equation of the line through (2, 5) and (6, 13).
Answer
Step 1: Find the slope first: m = (13 - 5) / (6 - 2) = 8 / 4 = 2 Step 2: Use point-slope form with (2, 5): y - 5 = 2(x - 2) Step 3: Expand: y - 5 = 2x - 4 Step 4: Add 5 to both sides: y = 2x + 1 Answe…
Find the equation of the line through (-1, 4) and (3, -8).
Answer
Step 1: Find slope: m = (-8 - 4) / (3 - (-1)) = -12 / 4 = -3 Step 2: Use point-slope form with (-1, 4): y - 4 = -3(x + 1) Step 3: Expand: y - 4 = -3x - 3 Step 4: Add 4 to both sides: y = -3x + 1 Answe…
Why is the slope of a vertical line undefined?
Answer
A vertical line is parallel to the Y-axis. Its slope is m = (y2 - y1) / (x2 - x1). For a vertical line, x1 = x2, so x2 - x1 = 0. Division by 0 is not defined. Therefore, the slope is undefined.
Why is the slope of a horizontal line 0?
Answer
A horizontal line is parallel to the X-axis. On such a line, y1 = y2. Using m = (y2 - y1) / (x2 - x1), the numerator becomes 0. So m = 0 / (x2 - x1) = 0, provided the denominator is not 0. Answer: The…
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