Lila planted a tree in her backyard. She made a graph to show the tree growth over 5 years.

1) What does the slope mean in real life in the context of the problem?

2) What does the y-intercept mean in real life in the context of the problem?

Answer in complete sentences.

Answer:

1. Growth rate of tree 3 ft per year, 2. Beginning height of tree 5 feet, rise/run = 3/1 = 3

Step-by-step explanation:

The solution is

1) The slope of the graph m = 3 represents the growth of the tree per year

2) The y-intercept means the initial height of the tree , when x = 0

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P = P ( 3 , 14 )

Let the second point be Q = Q ( 1 , 8 )

Now , the slope of the two points on the line is given by

Slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 14 - 8 ) / ( 3 - 1 )

Slope m = 6/2

Slope m = 3

Therefore , the slope is 3 feet per year

b)

The y intercept is calculated from the equation of line , when x = 0

So , the equation of line is given as

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 14 = 3 ( x - 3 )

On simplifying the equation , we get

y - 14 = 3x - 9

Adding 14 on both sides of the equation , we get

y = 3x + 5

Now , when x = 0

y = 3 ( 0 ) + 5

y = 5 feet

From the graph we can see that , at 0 years the initial height of the tree is also 5 feet

Therefore , the y intercept is 5 feet

Hence , The slope of the equation is 3 and y intercept is 5

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