The rate at which a plant grows is constant. at the 3rd week it is 12 inches tall and at the 5th week it is 20 inches tall. if this information is plotted on a coordinate plane, what is the y-coordinate of the the point (1, y)?

(3,12)(5,20)
slope = (20 - 12) / (5 - 3) = 8/2 = 4

y = mx + b
slope(m) = 4
use either of ur points (3,12)...x = 3 and y = 12
now we sub and find b, the y int
12 = 4(3) + b
12 = 12 + b
12 - 12 = b
0 = b

so ur equation is : y = 4x + 0...or just y = 4x

y = 4x......(1,y).....so x = 1
y = 4(1)
y = 4

so ur answer is (1,4).....this is basically saying that in the first week, the plant is 4 inches tall.

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MrRoyal MrRoyal · Answer 2 · 2021-12-16T04:01:22-05:00

The constant rate at which the plant grows is the slope of the coordinate plane.

The y-coordinate of the point (1,y) is 4

The ordered pair from the question can be represented as:

\((x,y)=(3,12)\ (5,20)\ (1,y)\)

The slope is calculated as:

\(m = \frac{y_2 -y_1}{x_2 - x_1}\)

So, we have:

\(m = \frac{20 -12}{5 -3}\)

\(m = \frac{8}{2}\)

\(m = 4\)

Also, the slope is:

\(m = \frac{20 -y}{5 -1}\)

\(m = \frac{20 -y}{4}\)

Equate both values of slope

\(\frac{20 -y}{4} = 4\)

Multiply both sides by 4

\(20 -y = 16\)

Collect like terms

\(y=20-16\)

\(y =4\)

Hence, the y-coordinate of the point (1,y) is 4