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A line in the xy-plane passes through the origin and has a slope of 1/7. Which of the following points lies on the line?
- a)(0, 7)
- b)(1, 7)
- c)(7, 7)
- d)(14, 2)
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
A line in the xy-plane passes through the origin and has a slope of 1/...
In the xy-plane, all lines that pass through the origin are of the form y = mx, where m is the slope of the line.
Therefore, the equation of this line is y = 1/7x, or x = 7y. A point with coordinates (a, b) will lie on the line if and only if a = 7b. Of the given choices, only choice D, (14, 2), satisfies this condition: 14 = 7(2).
Choice A is incorrect because the line determined by the origin (0, 0) and (0, 7) is the vertical line with equation x = 0; that is, the y-axis.
The slope of the y-axis is undefined, not 1/7. Therefore, the point (0, 7) does not lie on the line that passes the origin and has slope 1/7.
Choices B and C are incorrect because neither of the ordered pairs has a y-coordinate that is 1/7 the value of the corresponding x-coordinate.
Therefore, the equation of this line is y = 1/7x, or x = 7y. A point with coordinates (a, b) will lie on the line if and only if a = 7b. Of the given choices, only choice D, (14, 2), satisfies this condition: 14 = 7(2).
Choice A is incorrect because the line determined by the origin (0, 0) and (0, 7) is the vertical line with equation x = 0; that is, the y-axis.
The slope of the y-axis is undefined, not 1/7. Therefore, the point (0, 7) does not lie on the line that passes the origin and has slope 1/7.
Choices B and C are incorrect because neither of the ordered pairs has a y-coordinate that is 1/7 the value of the corresponding x-coordinate.
Most Upvoted Answer
A line in the xy-plane passes through the origin and has a slope of 1/...
To find the point that lies on the line passing through the origin with a slope of 1/7, we can use the equation of a line in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through the origin, the y-intercept is 0, so the equation becomes y = (1/7)x.
Let's check which of the given points satisfy this equation:
a) (0, 7)
If we substitute x = 0 and y = 7 into the equation, we get: 7 = (1/7)(0)
This equation is not true, so point (0, 7) does not lie on the line.
b) (1, 7)
Substituting x = 1 and y = 7 into the equation, we get: 7 = (1/7)(1)
This equation is true, so point (1, 7) lies on the line.
c) (7, 7)
Substituting x = 7 and y = 7 into the equation, we get: 7 = (1/7)(7)
This equation is true, so point (7, 7) lies on the line.
d) (14, 2)
Substituting x = 14 and y = 2 into the equation, we get: 2 = (1/7)(14)
This equation is true, so point (14, 2) lies on the line.
So, the points that lie on the line passing through the origin with a slope of 1/7 are (1, 7), (7, 7), and (14, 2). The correct answer is option D.
Let's check which of the given points satisfy this equation:
a) (0, 7)
If we substitute x = 0 and y = 7 into the equation, we get: 7 = (1/7)(0)
This equation is not true, so point (0, 7) does not lie on the line.
b) (1, 7)
Substituting x = 1 and y = 7 into the equation, we get: 7 = (1/7)(1)
This equation is true, so point (1, 7) lies on the line.
c) (7, 7)
Substituting x = 7 and y = 7 into the equation, we get: 7 = (1/7)(7)
This equation is true, so point (7, 7) lies on the line.
d) (14, 2)
Substituting x = 14 and y = 2 into the equation, we get: 2 = (1/7)(14)
This equation is true, so point (14, 2) lies on the line.
So, the points that lie on the line passing through the origin with a slope of 1/7 are (1, 7), (7, 7), and (14, 2). The correct answer is option D.
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Community Answer
A line in the xy-plane passes through the origin and has a slope of 1/...
In the xy-plane, all lines that pass through the origin are of the form y = mx, where m is the slope of the line.
Therefore, the equation of this line is y = 1/7x, or x = 7y. A point with coordinates (a, b) will lie on the line if and only if a = 7b. Of the given choices, only choice D, (14, 2), satisfies this condition: 14 = 7(2).
Choice A is incorrect because the line determined by the origin (0, 0) and (0, 7) is the vertical line with equation x = 0; that is, the y-axis.
The slope of the y-axis is undefined, not 1/7. Therefore, the point (0, 7) does not lie on the line that passes the origin and has slope 1/7.
Choices B and C are incorrect because neither of the ordered pairs has a y-coordinate that is 1/7 the value of the corresponding x-coordinate.
Therefore, the equation of this line is y = 1/7x, or x = 7y. A point with coordinates (a, b) will lie on the line if and only if a = 7b. Of the given choices, only choice D, (14, 2), satisfies this condition: 14 = 7(2).
Choice A is incorrect because the line determined by the origin (0, 0) and (0, 7) is the vertical line with equation x = 0; that is, the y-axis.
The slope of the y-axis is undefined, not 1/7. Therefore, the point (0, 7) does not lie on the line that passes the origin and has slope 1/7.
Choices B and C are incorrect because neither of the ordered pairs has a y-coordinate that is 1/7 the value of the corresponding x-coordinate.
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