Question

HELP ASAP I give total 100 points and big brain!! answer these pless

1.A system of equations consists of two lines. One line passes through (0, 4) and (1, 7) . The other line passes through (−1, −5) and (5, 13) .

Does the line through the first pair of points intersect the line through the second pair of points?
yes or no
2.
Select the correct choices to complete the sentence.
A system of equations consists of two lines. One line passes through (0, 2) and (9, −1) . The other line passes through (12, 7) and (−6, −5) .

Does the line through the first pair of points intersect the line through the second pair of points? yes or no

Answer 1

Slopes must not be equal to get intersection

#1

For first line

• m=7-4/1-0=3/1=3

For second

• m=13+5/5+1=18/6=3

No,Parallel

#2

First

• m=-1-2/9-0-3/-9=1/3

Second

• m=-5-7/-6-12=-12/-18=2/3

Yes, Intersect

Answer 2

Explanation:

Find the slopes of the lines and compare. The lines intersect if slopes are different.

Q1

Slopes are

• 
  `m_1= (7-4)/(1-0)=3\\`
• 
  `m_2= (13+5)/(5+1)=3\\`

Slopes are same, lines are parallel

Q2

Slopes are

• 
  `m_1= (-1-2)/(9-0)=-3/9=-1/3\\`
• 
  `m_2= (-5-7)/(-6-12)=-12/-18=2/3\\`

Lines intersect as slopes are different