Find the equation of straight line passing through the point (5, 4) and parallel to the line
2x + 3y + 7 = 0.
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2x+3y-22 = 0 is the equation parallel to 2x+3y+7=0 and passes through (5,4). ... Draw a parallel line with the same slope passing through (5,4). The y intercept is 8. The new equation is y= -2/3x +8.
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Given: A point (5, 4) and a straight line 2x + 3y + 7 = 0
To find: The equation of the line passing through the given point and parallel to the given line
Solution: Let us first find the slope of the given straight line.
2x + 3y + 7 = 0
⇒ 3y = -2x - 7
⇒ y = -2x/3 - 7/3
So the slope of this line is -2/3.
We know that the slope of two parallel lines are the same.
Hence the slope of the required line = -2/3.
As such, the equationof the required line :-
y - 4 = -2/3(x - 5)
⇒ -3(y - 4) = 2(x - 5)
⇒ -3y + 12 = 2x - 10
⇒ 2x + 3y - 22 = 0
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