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julia-pushkina [17]
3 years ago
12

The points (–8, –4) and (6, 10) fall on a particular line. What is its equation in slope-intercept form?

Mathematics
1 answer:
elena55 [62]3 years ago
6 0
First we need to use two point to find the slope (m)

m=(y2-y1)/(x2-x1)
X1=-8
Y1=-4
X2=6
Y2=10

m=(10-(-4))/(6-(-8))
m=(10+4)/(6+8)
m=14/14
m=1

Eq of the line formula :
Y-y1=m(x-x1)
Y-(-4)=1(x-(-8))
Y+4=x+8
Y=x+4
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Let's call a child's ticket c and an adult's ticket a. From this, we can say:

c + a = 116,

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Now, we are going to need to find another equation (the problem asks us to solve a systems of equations). This time, we are not going to base the equation on ticket quantity, but rather ticket price. We know that an adult's ticket is $17,000, and a child's ticket is thus

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Let's solve:

17000a + 12750c = 1653250

a = 116 - c

  • Find a on its own, which will allow us to substitute it into the first equation

17000(116 - c) + 12750a = 1653250

  • Substitute in 116 - c for a

1972000 - 17000c + 12750c = 1653250

  • Apply the Distributive Property

1972000 - 4250c = 1653250

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We have now found that 75 child's tickets were sold. Thus,

75 + a = 116 \Rightarrow a = 116 - 75 = 41,

41 adult tickets were sold as well.


In sum, 41 adult tickets were sold along with 75 child tickets.

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