The linear equation that gives the height on the x-th month is:
y = 2.5*x + 74.5
This will be modeled with a linear equation of the form:
y = a*x + b
Where a is the slope and b is the y-intercept.
Remember that for a line with the points (x₁, y₁) and (x₂, y₂), the slope is given by:
[tex]a = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
Here we have the two points (3, 82) and (7, 92). Where the first value is the number of months and the second value is the height.
So the slope is:
[tex]a = \frac{92 - 82}{7 - 3} = 10/4 = 2.5[/tex]
Then the linear equation is:
y = 2.5*x + b
To get the value of b, we use the fact that when x = 3, we have y = 82,
82 = 2.5*3 + b
82 = 7.5 + b
82 - 7.5 = b = 74.5
Then the linear equation is:
y = 2.5*x + 74.5
If you want to learn more about linear equations:
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