Question

One line passes through the points (−3,−1) and (1,−9). Another line passes through points (1,4) and (5,6). Are the lines parallel, perpendicular, or neither?

Answer 1

the two lines are perpendicular to one another

Explanation:

Find the slopes of the two lines and then compare them.

If the slopes are the same, the lines are parallel.

If the slopes are negative reciprocals, the lines are perpendicular.

If neither of these conditions hold, then the lines are neither parallel nor perpendicular.

(−3,−1) and (1,−9): As we go from the first point to the second, x (the "run") increases by 4 and y (the "rise") decreases by 8. Thus, the slope of the line through (−3,−1) and (1,−9) is m = rise / run = -8/4, or m = -2.

(1,4) and (5,6): As we go from the first to the second, x increeases by 4 and y increases by 2. Thus, the slope of the line through (1,4) and (5,6) is

m = rise / run = 2/4 = 1/2.

Because 1/2 is the negative reciprocal of -2, we know that the two lines are perpendicular to one another.

Answer 2

the lines are perpendicular

Explanation:

the first step to this question will be to find the slope intercept form of each of these lines. to do this we will first:

find the slope-

(-3,-1) and (1,-9)

y2-y1 / x2- x1

-9 - (-1) / 1 - (-3) (negative - negative = positive)

-8 / 4

therefore the slope is:

-2

we know that slope intercept form is y=mx+b

so.. y= -2x +______

I left the last part blank, because we only have the first half of the equation, now we will substitute the value of x and y into the equation from one of the coordinate points given above.

(-9) = -2(1) + _____

now we can simplify:

-9 = -2

this equation (-9 = -2) is not true, therefore we need to determine what we have to do to -2 to make it equal to -9.

-9 = -2 - 7 is true

therefore the answer is :

y= -2x-7

therefore the slope intercept form is y= -2x - 7

now that you know how to find the slope intercept form, you can find the other slope intercept form, and i'll provide the answer:

the slope intercept form you should find is

y=
`(1)/(2)`x +
`(7)/(2)`

now when we plot both of these lines we can see that:

the lines are perpendicular, meaning the lines pass through each other.