the table shows the height of a plant as it grows. write an equation in point-slope form that gives the plants heights at any time
time months: 2, 4, 6, 8
plant height: 18, 36, 54, 72
To write an equation in point-slope form, we need to use the formula:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line, and m is the slope of the line.
Using the points (2, 18) and (4, 36), we can find the slope:
m = (y₂ - y₁)/(x₂ - x₁)
= (36 - 18)/(4 - 2)
= 18/2
= 9
Now we can select any of the given points to plug into the equation. Let's use (2, 18):
y - 18 = 9(x - 2)
Simplifying the equation, we get:
y - 18 = 9x - 18
y = 9x
Therefore, the equation in point-slope form that gives the plant's heights at any time is:
height = 9(time months)