Question

A line passes through the point (0, 1) and has a positive slope. Which of these points could that line NOT pass through? Check all that apply.
(12, 3)
(–2, –5)
(–3, 1)
(1, 15)
(5, –2)

Answer 1

We have to find slopes one by one.

$\\ \sf\longmapsto Slope=m=\dfrac{y_2-y_1}{x_2-x_1}$

#1

• (0,1)
• (12,3)

$\\ \sf\longmapsto \dfrac{3-1}{12-0}$

$\\ \sf\longmapsto \dfrac{2}{12}$

$\\ \sf\longmapsto \dfrac{1}{6}>0$

• Line passes through this.

#2

• (-2,-5)

$\\ \sf\longmapsto \dfrac{-5-1}{-2-0}$

$\\ \sf\longmapsto \dfrac{-6}{-2}$

$\\ \sf\longmapsto 3>0$

• Line passes through this

#3

• (-3,1)

$\\ \sf\longmapsto \dfrac{1-1}{-3-0}$

$\\ \sf\longmapsto \dfrac{0}{-3}=0$

• Not possible (Line passes through y axis as one co-ordinate is (0,1))

#4

• ( 1,15)

$\\ \sf\longmapsto \dfrac{15-1}{1-0}$

$\\ \sf\longmapsto \dfrac{14}{1}$

$\\ \sf\longmapsto 14>0$

• Line passes through this

#5

• (5,-2)

$\\ \sf\longmapsto \dfrac{-2-1}{5-0}$

$\\ \sf\longmapsto \dfrac{-3}{5}$

• Line doesnot pass through this.

Answer 2

We have to find slopes one by one.

#1

(0,1)

(12,3)

Line passes through this.

#2

(-2,-5)

Line passes through this

#3

(-3,1)

Not possible (Line passes through y axis as one co-ordinate is (0,1))

#4

( 1,15)

Line passes through this

#5

(5,-2)

Therefore, The Line does not pass through this.