Question

On the coordinate plane, line
j
passes through the points
(
−
16
,
3
)
and
(
0
,
35
)
. Line
k
passes through the points
(
−
10
,
5
)
and
(
26
,
−
13
)
.



Which TWO statements about the lines are TRUE?

A.
An equation for line
j
is
2
x
−
y
=
35
.

B.
An equation for line
k
is
y
=
−
0.5
x
.

C.
The lines intersect at
x
=
−
23
1
3
.

D.
The lines intersect at
x
=
−
14
.

E.
The lines do not intersect

Answer 1

B and D.

Work:
- Line j through (-16,3) and (0,35): slope = (35−3)/(0−(−16)) = 32/16 = 2, so y = 2x + 35. (A is 2x−y=35 ⇔ y=2x−35, wrong.)
- Line k through (−10,5) and (26,−13): slope = (−13−5)/(26−(−10)) = −18/36 = −1/2 and b = 0, so y = −0.5x. (B true.)
- Intersection: 2x + 35 = −0.5x ⇒ 2.5x = −35 ⇒ x = −14. (D true; C and E false.)