Respuesta :
The line will have the same slope as line m.
Slope of line m = (2 - -3) / (2 - 1) = 5
The answer is (0, 0) and (1, 5) which has slope (5-0) / (1 - 0) = 5 also.
Slope of line m = (2 - -3) / (2 - 1) = 5
The answer is (0, 0) and (1, 5) which has slope (5-0) / (1 - 0) = 5 also.
The pairs of points (0, 0) and (1, 5) define a line parallel to line m.
The correct answer is option (f).
What are parallel lines?
"The lines in a plane that are always the same distance apart and never intersect."
The formula to find the slope of the line:
If a line passes through points [tex](x_1,y_1),(x_2,y_2)[/tex]then the slope of the line is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
For given question,
Line m contains points (1, -3) and (2, 2).
So, the slope of the lime m would be,
[tex]m_1=\frac{2-(-3)}{2-1}\\\\ m_1=\frac{2+3}{1}\\\\ m_1=5[/tex]
We know, the slope of the parallel lines are equal.
So, we find the slope of each line for given pairs of points and then find the required parallel line.
1) (0, 0) and (1, 5)
slope = (5 - 0)/(1 - 0)
slope = 5
slope = m1
2) (1, 1) and (6, 2)
slope = (2 - 1)/(6 - 1)
slope = 1/5
slope ≠ m1
3) (0, 0) and (-1, 1)
slope = (1 - 0)/(-1 - 0)
slope = -1
slope ≠ m1
4) (-4, 0) and (5, 5)
slope = (5 - 0)/(5 - (-4))
slope = 5/9
slope ≠ m1
Therefore, the pairs of points (0, 0) and (1, 5) define a line parallel to line m.
The correct answer is option (f).
Learn more about parallel lines here:
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