Answer:
the answers are bolded below!
Step-by-step explanation:
1. y-y1=m(x-x1)
line one- 14-4/6-1 = 10/5 = 2
so.... y-1=2(x-4)
simplified y=2x-7
line two- -2-23/1-6 = -25/5 = -5
so..... y-6=-5(x-23)
simplified y=-5x+121
b- they will intersect 1 time at (18.2,29.5)
2. No, it the system has infinitely many solutions, then the lines would be on top of each other. But since there are only two solutions, then your answer would not be infinitely many solutions.
3. y=-2x+1. This would not intersect with y=-2x+3 because they are parallel. the slopes are the same so they will each travel at the same rate but they have different y intercepts.
4. y=-2x+7 ------> x=-1/2y-7/2
y=-3(-1/2y+7/2)+8 -----> y=5
y=-2x+7 ---> 5=-2x+7 ----> x=1
one solution at (1,5) because f graphed, the lines would only intersect once.
b- x=5
3x-y=5 ---> 3(5)-y=5 ---> y=10
one solution at (5,10) because f graphed, the lines would only intersect once.
c- no solutions because if it were to be graphed, the lines would not intersect at all.
d- no solutions because if it were to be graphed, the lines would not intersect at all.
e- no solutions because if it were to be graphed, the lines would not intersect at all.
i am in algebra two so you can trust my answer. If you need more help lmk in the comments. Happy holidays and stay safe!
