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<span>find the equations of the lines in slope-intercept form which is y=mx+b where m=slope b=y intercept
the choices:
0 solutions: means the lines don't intercect at all, meaning same slope but different y intercept or they ar paralell
1 solution: lines intercect in 1 point
2 solutions: curvy line with a straight line thorugh middle
infinetly solutions: same line
to find slope you do
slope=(y1-y2)/(x1-x2)
first line is
(-4,8)
(4,6)
(x,y)
x1=-4
y1=8
x2=4
y2=6
subsitute
(8-6)/(-4-4)=2/-8=-1/4
slope=-1/4
subsitute
y=-1/4x+b
subsitute one of the points
(4,6)
x=4
y=6
6=-1/4(4)+b
6=-1+b
add 1 to both sides
7=b
y=-1/4+7
now solve for the other equation
(-1,1)
(3,5)
x1=-1
y1=1
x2=3
y2=5
subsitute
(1-5)/(-1-3)=(-4)/(-4)=4/4=1
y=1x+b
subsitute
(-1,1)
x=-1
y=1
1=1(-1)+b
1=-1+b
add 1
2=b
y=x+2
we have the lines
y=-1/4x+7 and
y=x+2
solve for a common solution
y=x+2 and y=-1/4x+7 therefor
x+2=-1/4x+7
subtract 7 from both sides
x-5=-1/4x
mulitply both sides by -4
-4x+20=x
add 4x to both sides
20=5x
divide both sides by 5
4=x
subsitute
y=x+2
y=4+2
y=6
the soluiton is (4,6)
there is only one solution
the answer is B</span>
The equation that models the students is a linear equation
The equation that models the number of students in each bus is 6x = 216, and the number of students in each bus is 36
<h3>How to determine the equation?</h3>
The given parameters are:
Students = 221
Van = 5
The rest students = 6 buses
Start by calculating the number of students remaining:
Remaining students = 221 - 5
Remaining students = 216
Represent the number of students in each bus with x.
So, we have:
6 buses * x = Remaining students
This gives
6x = 216
Divide both sides by 6
x = 36
Hence, the equation that models the number of students in each bus is 6x = 216, and the number of students in each bus is 36
Read more about linear equations at:
brainly.com/question/15602982
You can use the distributive property of multiplication over addition to find the equivalent expression to the given expression.
The expression which is equivalent to the given expression is given by
Option D: 
<h3>What are equivalent expressions?</h3>
Those expressions who might look different but their simplified forms are same expressions are called equivalent expressions.
<h3>What is distributive property of multiplication over addition?</h3>
Suppose a, b and c are three numbers. Then we have:
(a(b+c) means a multiplied to (b+c). The sign of multiplication is usually hidden when using symbols and both quantities which are in multiplication are written together without space)
<h3>Using the above property and the fact that 28 and 35 are multiples of 7 to get the equivalent expression</h3>
The given expression is 
Since 28 = 7 times 4 and 35 = 7 times 5
Thus,
Thus,
The expression which is equivalent to the given expression is given by
Option D:
Learn more about equivalent expressions here:
brainly.com/question/10628562
270(pi/180)=3pi/2=theta
theta*radius=arc length
(3pi/2)(14)=65.9734 yds
