Question

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) 2, 4, 6, 8
Heigh (inches) 14, 23, 32, 41

Answer 1

Let's start by determining the slope of the equation. We can find the change in height over the change in time using any two points:

Slope = (41 - 14) / (8 - 2) = 27 / 6 = 4.5

Now, let's use the point-slope form of a line, y - y1 = m(x - x1), where (x1, y1) is the coordinates of one of the points (2, 14):

y - 14 = 4.5(x - 2)

Simplifying, we have:

y - 14 = 4.5x - 9

Now, let's rewrite the equation in slope-intercept form, y = mx + b, by isolating y:

y = 4.5x - 9 + 14
y = 4.5x + 5

Therefore, the equation in slope-intercept form that gives the tree's height at any time is y = 4.5x + 5.