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08 Dec 2023, 10:43
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Perpendicular: \(3x=8+2y\)
Parallel: \(3y=-2x-12\)
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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Data Insights (DI) Butler 2023-24 [Question #148, Date: Dec-08-2023] [Click here for Details]
In the table, select an equation whose graph is a line perpendicular to the graph of the equation \(2x + 3y – 5 = 0\), and an equation whose graph is a line parallel to the graph of the equation \(2x + 3y – 5 = 0.\) Make only one selection in each column.
| Perpendicular | Parallel | |
| \(y=(x+2)(x-3)\) | ||
| \(3x=8+2y\) | ||
| \(\frac{(2x+3y)}{5}\) | ||
| \(y=\frac{2}{3}x+\frac{5}{3}\) | ||
| \(3y=-2x-12\) | ||
| \(3x+2y-2=0\) |
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Official Answer
Perpendicular: \(3x=8+2y\)
Parallel: \(3y=-2x-12\)
08 Dec 2023, 23:29
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Equation of two lines of the form:
ax + by + c = 0
Ax + By + C = 0
They are parallel if:
a = nA and b = nB
This is satisfied in option 4 after rearrangement.
The lines are parallel is (a)(A) + (b)(B) = 0
This is satisfied in option 2
ax + by + c = 0
Ax + By + C = 0
They are parallel if:
a = nA and b = nB
This is satisfied in option 4 after rearrangement.
The lines are parallel is (a)(A) + (b)(B) = 0
This is satisfied in option 2
09 Dec 2023, 04:16
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When two lines are perpendicular to each other then the product of their slopes is equal to -1.
When two lines are parallel to each other then both have the same slope.
2x+3y-5=0 (let's rearrange the equation in the form of the equation of a line)
3y=-2x+5
y=-2x/3+5/3
Slope of line = m1 = -2/3
Therefore, the slope of the perpendicular line must be:
m1*m2=-1
-2/3*m2=-1
m2=3/2 (option 2)
Slope of line that is parallel to the above line must be same i.e -2/3 (option 5)
When two lines are parallel to each other then both have the same slope.
2x+3y-5=0 (let's rearrange the equation in the form of the equation of a line)
3y=-2x+5
y=-2x/3+5/3
Slope of line = m1 = -2/3
Therefore, the slope of the perpendicular line must be:
m1*m2=-1
-2/3*m2=-1
m2=3/2 (option 2)
Slope of line that is parallel to the above line must be same i.e -2/3 (option 5)
