Question

You plant two flowers in a garden. The equations y equals 11.3 x plus 18 and y equals 5.3 x plus 18 model the heights y of the​ flowers, in​ millimeters, after x days. What does the​ y-intercept of each equation​ represent? Will the flowers ever be the same​ height?
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Part 1
What does the​ y-intercept of each equation​ represent?
The difference of the​ flowers' heights
The rate of growth of the flower
The height of the flower when planted
The height of the flower after 10 days

Answer 1

The y-intercept is the height when x = 0, i.e. the initial height when planted: 18 mm for each flower.

Set the heights equal: 11.3x + 18 = 5.3x + 18 → 6x = 0 → x = 0.
So the flowers are the same height only at planting (day 0); after that the first flower (11.3 mm/day) grows faster and is taller.