Answer: Tree A will be the tallest tree after 6 months. Tree A will be 29 inches, Tree B will be 20 inches, and Tree C will be 12 inches.
Step-by-step explanation:
To answer this question, we will create an equation for all of the trees, substitute in the time of six months, and see which height is the tallest.
We will write the first two equations in slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept. We will create the third equation in point-slope form, y - y1 = m(x - x1), where (x1, y1) is a coordinate point of the function and m is the slope.
Tree A: y = 4x + 5
We are given that the slope is 4 (4 inches every month) and that the y-intercept is 5 (5 inches when it was first planted).
y = 4x + 5
Tree B: y = 3x + 2
We will use the slope formula to find the slope.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} } =\frac{20-17}{7-6}=\frac{3}{1} =3[/tex]
The line has a slope of 3 with a y-intercept at (0, 2).
y = 3x + 2
Tree C: y - 12 = [tex]\frac{20}{3}[/tex](x - 60)
We will use the slope formula to find the slope, as we did with Tree B.
[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1} } =\frac{60-10}{12-4.5}=\frac{50}{7.5} =6\frac{2}{3}\;\;or\;\;\frac{20}{3}[/tex]
Using the point (60, 12) from the table and the slope we found, we can create a point-slope form equation.
y - 12 = [tex]\frac{20}{3}[/tex](x - 60)
Now, we will substitute 6 months into each equation. Let x be the time passed in months and y be the height of the tree at x time.
Tree A ➜ y = 4x + 5 ➜ y = 4(6) + 5 ➜ y = 29 inches
Tree B ➜ y = 3x + 2 ➜ y = 3(6) + 2 ➜ y = 20 inches
Tree C ➜ y - 12 = [tex]\frac{20}{3}[/tex](x - 60) ➜ y - 12 = [tex]\frac{20}{3}[/tex](60 - 60) ➜ y = 12 inches
Tree A will be the tallest tree after 6 months.
