Mathematics
Grade10
Easy
Question
Write the equation in point-slope form for the line that contains the points
(3, -5) and (5, - 1)
- y - 5 = 2(x + 3)
- y + 5 = 2(x - 3)
- y - 3 = 2(x + 5)
- y + 3 = 2(x - 5)
Hint:
Slope of a line that passes through (x1,y1), (x2, y2)
![m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction](data:image/png;base64,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)
Point-slope form of equation of a line is y - y1 = m (x - x1)
The correct answer is: y + 5 = 2(x - 3)
Given The points (3, -5) and (5, - 1).
Step1 : calculating slope
Slope of a line that passes through (x1,y1), (x2, y2)
![m equals fraction numerator y subscript 2 minus y subscript 1 over denominator x subscript 2 minus x subscript 1 end fraction](data:image/png;base64,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)
=![left parenthesis negative 1 plus 5 right parenthesis divided by left parenthesis 5 minus 3 right parenthesis](data:image/png;base64,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)
=2
Step 2 : making point slope form
Point-slope form of equation of a line is y - y1 = m (x - x1)
Substitute point (3, -5) and m value.
y + 5 = 2 (x -3)
y + 5 = 2 (x -3) , is desired equation .
First calculate the slope making use of two points
and then using slope and point construct the equation of line.