The table shows the height of a plant as it grows. Which equation in point-slope form gives the plant’s height at any time?
x - 3, 5, 7, 9
y - 21, 35, 49, 63
The formula for the linear equation in point-slope form is y - y1 = m(x - x1), where (x1, y1) is one of the points on the line and m is the slope of the line.
Given the points (x1, y1) = (3, 21) and (x2, y2) = (9, 63), we can calculate the slope m:
m = (y2 - y1) / (x2 - x1)
m = (63 - 21) / (9 - 3)
m = 42 / 6
m = 7
Using the point-slope form, the equation is then:
y - 21 = 7(x - 3)
So, the equation in point-slope form that gives the plant's height at any time is y - 21 = 7(x - 3).