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Equation of Line Flashcards.
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Which ONE of these statements about the lines defined by the following equations is TRUE?
Line 1: y=23x+12
Line 2: y=−32x−12
Which ONE of these statements about the lines defined by the following equations is TRUE?
Line 1: y...
Correct answer:
The lines intersect and are perpendicular.
Explanation:
The TRUE statement:
"The lines intersect and are perpendicular." This is true because the slopes of the two lines are opposite-reciprocals of each other.
m_1=frac{2}{3} textup{and} m_2=-frac{3}{2}
The FALSE statements:
"The lines intersect at the point (0,−8)." The lines actually intersect at the point (−8,0). Neither line touches the point (0,−8), as their y-intercepts are given in their respective equations as (0,12) and (0,−12).
"The slopes of the two lines are identical." This is not true because the slope of Line 1 is 23 whereas the slope of Line 2 is −32.
"The lines do not intersect." The lines would need to be parallel (i.e., have the same slope) for this to be the case, but the lines do not have the same slope.
"The lines intersect only once because they are parallel." Parallel lines never intersect, so this statement cannot be made of any set of two lines.
Determine if the lines y=x+3y=x+3 and y=−x+10y=−x+10 are perpendicular.
Determine if the lines y=x+3y=x+3 and y=−x+10y=−x+10 are perpendicular.
Correct answer:
The lines are perpendicular
Explanation:
For lines to be perpendicular, the slopes need to be negative reciprocals of each other. For the line y=x+3y=x+3, the slope is 1. For a line to be perpendicular to it, it will need to have a slope of −11=1−11=1. Since the line y=−x+10y=−x+10 has a slope of -1, the lines are perpendicular to each other.
Determine if the lines y=x+3y=x+3 and y=−x+10y=−x+10 are perpendicular.
Determine if the lines y=x+3y=x+3 and y=−x+10y=−x+10 are perpendicular.
Correct answer:
The lines are perpendicular
Explanation:
For lines to be perpendicular, the slopes need to be negative reciprocals of each other. For the line y=x+3y=x+3, the slope is 1. For a line to be perpendicular to it, it will need to have a slope of −11=1−11=1. Since the line y=−x+10y=−x+10 has a slope of -1, the lines are perpendicular to each other.
Which of these lines is perpendicular to y=−3x+6?
Which of these lines is perpendicular to y=−3x+6?
Correct answer:
y=13x−9
Explanation:
Perpendicular lines have slopes that are negative reciprocals of one another. Since all of these lines are in the y=mx+b format, it is easy to determine their slopes, or m.
The slope of the original line is −3, so any line that is perpendicular to it must have a slope of 13.
The only line with a slope of 13 is y=13x−9.
Which ONE of these statements about the lines defined by the following equations is TRUE?
Line 1: y=23x+12
Line 2: y=−32x−12
Which ONE of these statements about the lines defined by the following equations is TRUE?
Line 1: y...
Correct answer:
The lines intersect and are perpendicular.
Explanation:
The TRUE statement:
"The lines intersect and are perpendicular." This is true because the slopes of the two lines are opposite-reciprocals of each other.
m_1=frac{2}{3} textup{and} m_2=-frac{3}{2}
The FALSE statements:
"The lines intersect at the point (0,−8)." The lines actually intersect at the point (−8,0). Neither line touches the point (0,−8), as their y-intercepts are given in their respective equations as (0,12) and (0,−12).
"The slopes of the two lines are identical." This is not true because the slope of Line 1 is 23 whereas the slope of Line 2 is −32.
"The lines do not intersect." The lines would need to be parallel (i.e., have the same slope) for this to be the case, but the lines do not have the same slope.
"The lines intersect only once because they are parallel." Parallel lines never intersect, so this statement cannot be made of any set of two lines.
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