Answer:
option B A line passing through points (1,10) and (0,8)
option D A line passing through points (4,2) and (8,10)
Step-by-step explanation:
we know that
If two lines are parallel , then their slopes are the same
In this problem we have
[tex]y=2x-4[/tex]
The slope is equal to
[tex]m=2[/tex]
Remember that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Verify each case
case A) A line passing through points (0,6) and (2,2)
substitute in the formula
[tex]m=\frac{2-6}{2-0}[/tex]
[tex]m=\frac{-4}{2}[/tex]
[tex]m=-2[/tex]
Compare with the slope of the given line (m=2)
[tex]-2\neq2[/tex]
therefore
This line is not parallel to the given line
case B) A line passing through points (1,10) and (0,8)
substitute in the formula
[tex]m=\frac{8-10}{0-1}[/tex]
[tex]m=\frac{-2}{-1}[/tex]
[tex]m=2[/tex]
Compare with the slope of the given line (m=2)
[tex]2=2[/tex]
therefore
This line is parallel to the given line
case C) A line passing through points (10,1) and (8,0)
substitute in the formula
[tex]m=\frac{0-1}{8-10}[/tex]
[tex]m=\frac{-1}{-2}[/tex]
[tex]m=0.5[/tex]
Compare with the slope of the given line (m=2)
[tex]0.5\neq2[/tex]
therefore
This line is not parallel to the given line
case D) A line passing through points (4,2) and (8,10)
substitute in the formula
[tex]m=\frac{10-2}{8-4}[/tex]
[tex]m=\frac{8}{4}[/tex]
[tex]m=2[/tex]
Compare with the slope of the given line (m=2)
[tex]2=2[/tex]
therefore
This line is parallel to the given line
