The table shows the height of a tree as it grows. What equation in slope-intercept form gives the tree's height at any time?
Time
(months) Height
(inches)
2 14
4 23
6 32
8 41
(1 point)
Responses
a. y = 9x + 2
b. y = 9 over 2x + 5
c. y = 9 over 2x
d. y = 5x + 9 over 2
To find the equation in slope-intercept form for the height of the tree at any time, we can use the two points given (2, 14) and (4, 23) to find the slope and then use one of the points to solve for the y-intercept.
First, calculate the slope:
Slope = (23 - 14) / (4 - 2) = 9 / 2
Now, use the point-slope form of a linear equation to find the y-intercept:
y - 14 = (9 / 2)(x - 2)
y - 14 = 9 / 2 * x - 9
y = 9 / 2 * x - 9 + 14
y = 9 / 2 * x + 5
The equation in slope-intercept form is:
y = 9 / 2 * x + 5
Therefore, the correct answer is:
b. y = 9 over 2x + 5