Find the equation of the line passing through the point (-4, 4) and is perpendicular to the line y = 2x - 5.
1 answer:
Answer: y = (-1/2)x + 2
Concept:
When two lines are perpendicular to each other, their slopes are negative reciprocals.
The reciprocal of a number is 1 divided by the number.
In other words, it is the image opposite of a term.
Solve:
<u>Given information</u>
Given line = y = 2x - 5
Point = (-4, 4)
<u>Find the slope of the line</u>
Given the line is perpendicular to the line y = 2x - 5, the slope of the line would be negative reciprocal of the line y = 2x - 5.
Slope of line [y = 2x - 5] = 2
Slope of new line = (-1/2)
<u>Find the y-intercept by substituting the given point</u>
Equation of the new line: y = (-1/2)x + b
- b = y-intercept
y = (-1/2)x + b
4 = (-1/2) (-4) + b
4 = 2 + b
4 - 2 = 2 + b - 2
b = 2
<u>Finalize the equation of the line</u>
Slope = -1/2
Y-intercept = 2
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Answer:
option B
Step-by-step explanation:
Given :
Step 1 : simplify the equation :
Step 2: Arrange the terms :
Step 3 : Solve for x and y :
2x - 3y = - 9 ------ ( 1 )
5x - 2y = - 7 --------- ( 2 )
_____________________
( 1 ) x 5 => 10x - 15y = - 45 ---------- (3 )
( 2) x 2 => 10x - 4y = - 14 ----------- (4 )
_______________________
( 3 ) - ( 4 ) => 0x - 11y = - 31
- 11 y = - 31
Substitute y in ( 1 ) :
2x - 3y = - 9
Therefore the solution to the sytem is
The solution of the system of equation is a point which lies
on the both the lines.
Option A : False , It says the solution lies above one of the given line.
But the solution of the system of equation always lies on
both the line.
Option B : True , says the solution is a point on the coordinate plane.
Option C : False, because if the solution is on the x-axis , then
the y coordinate in the solution would be zero.
But it is not zero.
Option D : False , the solution is the point where both the lines intersect.