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A line passes through #(2 ,8 )# and #( 1, 5 )#. A second line passes through #( 6, 1 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

James Atkins

#color(violet)("One other point on the second line is " (7,4)#

#"Slope of line 1 " = m = (y_2 - y_1) / (x_2 - x_1) = (5-8) / (1-2) = 3#

As #2^(nd)# line is parallel to the first line, slope of second line also #3#

#"Equation of second line in point - slope form is "

#(y - 1) = 3 * (x - 6)#

#3x - y = 17#

Let y = 4. Then x = 7#

#color(violet)("One other point on the second line is " (7,4)#

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Answer 2

Ella Armstrong

The second line may pass through any point with the same vertical distance from the first line as the point (6, 1). One such point would be (7, -2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.