Question

6. Line 1 passes through the points (1,4) and (-2,5). Line 2 passes through the points (1,0) and (0,3). What is true about Line 1 and Line 2? (2 points) (A) (B) They are perpendicular. They are parallel. They both decrease. They both increase. (C) (D)

Answer 1

First, calculate the slope (m) of both lines.

`m=(y2-y1)/(x2-x1)`

Line 1:

Point 1 = (x1,y1) = (1,4)

Point 2 = (x2,y2) = (-2,5)

Replacing:

`m=(5-4)/(-2-1)=(1)/(-3)=-(1)/(3)`

Line 2:

Point 1 = (x1,y1) = (1,0)

Point 2 = (x2,y2) = (0,3)

`m=(3-0)/(0-1)=(3)/(-1)=-3`

Lines to be parallel must have the same slope, and to be perpendicular, they must have negative reciprocal slope.

None of the slopes are equal or negative reciprocal. SO, A and B are false-

Now, for the increase/ decrease

We can see that both lines have a negative slope, so they both decrease.

Correct option: C