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Find the equation of the line joining the point (3, 5) with the point of intersection 2x+3y-5=0 and 3x+5y-7=0.
- a)6x+y+23=0
- b)6x+y-23=0
- c)6x+2y+14=0
- d)2x+5y+5=0
Correct answer is option 'B'. Can you explain this answer?
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Find the equation of the line joining the point (3, 5) with the point ...
To find the equation of the line joining the point (3, 5) with the point of intersection of 2x + 3y - 5 = 0 and 3x + 5y - 7 = 0, we need to follow the steps given below:
Step 1: Find the point of intersection of the two lines 2x + 3y - 5 = 0 and 3x + 5y - 7 = 0.
Multiplying the first equation by 5 and the second equation by 3, we get:
10x + 15y - 25 = 0
9x + 15y - 21 = 0
Subtracting the second equation from the first, we get:
x = 4
Substituting x = 4 in either of the two equations, we get:
y = -1
Therefore, the point of intersection is (4, -1).
Step 2: Find the slope of the line joining the two points (3, 5) and (4, -1).
Using the formula for slope, we get:
slope = (y2 - y1)/(x2 - x1)
= (-1 - 5)/(4 - 3)
= -6
Step 3: Use the point-slope form of the equation of a line to find the equation of the line passing through the point (3, 5) with slope -6.
Using the point-slope form, we get:
y - 5 = -6(x - 3)
Simplifying and rearranging, we get:
y = -6x + 23
Therefore, the equation of the line joining the point (3, 5) with the point of intersection of 2x + 3y - 5 = 0 and 3x + 5y - 7 = 0 is 6x - y - 23 = 0, which is option B.
Step 1: Find the point of intersection of the two lines 2x + 3y - 5 = 0 and 3x + 5y - 7 = 0.
Multiplying the first equation by 5 and the second equation by 3, we get:
10x + 15y - 25 = 0
9x + 15y - 21 = 0
Subtracting the second equation from the first, we get:
x = 4
Substituting x = 4 in either of the two equations, we get:
y = -1
Therefore, the point of intersection is (4, -1).
Step 2: Find the slope of the line joining the two points (3, 5) and (4, -1).
Using the formula for slope, we get:
slope = (y2 - y1)/(x2 - x1)
= (-1 - 5)/(4 - 3)
= -6
Step 3: Use the point-slope form of the equation of a line to find the equation of the line passing through the point (3, 5) with slope -6.
Using the point-slope form, we get:
y - 5 = -6(x - 3)
Simplifying and rearranging, we get:
y = -6x + 23
Therefore, the equation of the line joining the point (3, 5) with the point of intersection of 2x + 3y - 5 = 0 and 3x + 5y - 7 = 0 is 6x - y - 23 = 0, which is option B.
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Find the equation of the line joining the point (3, 5) with the point ...
Substitute (3,5) in the given 4 options . it will satisfy any one.
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Find the equation of the line joining the point (3, 5) with the point of intersection 2x+3y-5=0 and 3x+5y-7=0.a)6x+y+23=0b)6x+y-23=0c)6x+2y+14=0d)2x+5y+5=0Correct answer is option 'B'. Can you explain this answer?
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