Question

Line L passes through the points

(
−
3
,
2
)
and
(
5
,
−
1
)
. Line M has the equation below.

y
=
2
3
x
−
4

Which statement is true?

A.
Line L has a negative slope and line M has a positive slope.

B.
Line L has a positive slope and line M has a negative slope.

C.
Both lines have negative slopes.

D.
Both lines have positive slopes.

Answer 1

The statement A. Line L has a negative slope and line M has a positive slope is true .

To determine the slope of Line L, we can use the formula:

Slope= Change in y/ Change in x

For Line L, using the given points (−3,2) and (5,−1):

Slope of L= (−1−2) / (5−(−3))

= −3 / 8

Now, let's compare this with the slope of Line M, which is given by

y= 2/3x−4.

The coefficient of x (the number in front of x) represents the slope.

For Line M, the slope is 2/3 .

Now, comparing the slopes:

Slope of L=− 3/8

​Slope of M= 2/3

So, the correct statement is:

A. Line L has a negative slope, and line M has a positive slope.

Therefore, option A is true.