Question

Please no trolls! I need the right answer!

the cost of admission to a concert is $65 for 3 children and 5 adults, if x is the cost of 1 child and y is the cost of one adult, write a liner equation in slope-intercept form to represent this situation.

Answer 1

Answer: y = (-3/5)x + 13

This is the same as writing
`\text{y} = -(3)/(5)\text{x}+13`

note: -3/5 = -0.6

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Work Shown:

x = cost of 1 child

y = cost of 1 adult

3x = cost of 3 children

5y = cost of 5 adults

3x+5y = total cost of everyone mentioned so far

3x+5y = 65 dollars

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Let's solve for y to get it into slope intercept form (y = mx+b)

3x+5y = 65

5y = -3x+65

y = (-3x+65)/5

y = (-3x)/5 + 65/5

y = (-3/5)x + 13 is the final answer.

This is now in y = mx+b form

• m = -3/5 = slope
• b = 13 = y intercept

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Optional Section:

If you wanted to graph this equation, then plug in x = 0 to find that y = 13.

One point on the line is (0,13) which is the y intercept. We can quickly determine this by looking at the last value of y = (-3/5)x+13.

Then starting at the y intercept location, move down 3 and to the right 5 to arrive at (5, 10) as another point on the line. This "down 3, right 5" motion is directly due to the slope -3/5

• slope = -3/5 = rise/run
• rise = -3 = go down 3
• run = 5 = go to the right 5

In summary, the two points (0,13) and (5,10) are on the straight line.