Final Answer:
a. $ y = 2000x + 4000 $
b. (Graph: line with y-intercept at 4000 and slope 2000 — rises 2000 units for each 1 unit right)
c. $12,000
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Explanation:
Let’s break down problem 43 step by step.
a. We need an equation in slope-intercept form: $ y = mx + b $.
- $ y $ = total cost (in dollars)
- $ x $ = number of hours filming
- The basic fee is $4000 — that’s what you pay even if $ x = 0 $, so that’s the
y-intercept, $ b = 4000 $.
- The per-hour charge is $2000 — that means for each extra hour, cost goes up by $2000. So the
slope $ m = 2000 $.
→ Plug into the formula: $ y = 2000x + 4000 $.
b. To graph it:
- Start at (0, 4000) on the y-axis (that’s the basic fee).
- From there, go right 1 unit (1 hour), up 2000 units (since slope = 2000/1). Plot (1, 6000).
- Draw a straight line through those points.
c. For 4 hours: plug $ x = 4 $ into the equation:
$ y = 2000(4) + 4000 = 8000 + 4000 = 12{,}000 $.
So the cost is $12,000.
Parent Tip: Review the logic above to help your child master the concept of slopes and intercepts worksheet answers.
