The table shows the height of a plant as it grows what equation in point slope form gives the plant height at any time let y stand for the height of the plant in cm and let x stand for the time in months
(3,15),(5,25),(7,35),(9,45)
To find the equation of the line in point-slope form, we need to find the slope (m) and one point on the line.
The slope (m) can be found using the formula:
m = (change in y) / (change in x)
Let's choose two points to find the slope:
(3, 15) and (9, 45)
m = (45 - 15) / (9 - 3)
m = 30 / 6
m = 5
Now we have the slope (m = 5) and one point (3, 15).
Using the point-slope form, we have:
y - y1 = m(x - x1)
Substituting the values, we have:
y - 15 = 5(x - 3)
Simplifying the equation, we get:
y - 15 = 5x - 15
Therefore, the equation in point-slope form is:
y = 5x
To find the equation in point-slope form, we need to start by finding the slope (m) using two points from the table.
Let's choose points (3, 15) and (9, 45):
m = (y2 - y1) / (x2 - x1)
m = (45 - 15) / (9 - 3)
m = 30 / 6
m = 5
Now that we have the slope (m), we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Let's choose point (3, 15) as our reference point:
y - 15 = 5(x - 3)
Simplifying it further:
y - 15 = 5x - 15
Therefore, the equation in point-slope form that represents the plant's height at any time is:
y = 5x
Note: This equation assumes that the plant's height increases by 10 cm every 2 months consistently.
To find the equation in point-slope form that gives the plant height at any time, you need to use the given points on the table. Point-slope form of the linear equation is given as y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.
First, let's calculate the slope (m) using any two points on the line. Let's choose the points (3, 15) and (5, 25):
m = (y2 - y1) / (x2 - x1)
= (25 - 15) / (5 - 3)
= 10 / 2
= 5
Now we have the slope (m = 5). Let's choose one point from the table, for example, (3, 15). We can substitute this point and the slope into the point-slope form equation to get the equation for the plant height:
y - y1 = m(x - x1)
y - 15 = 5(x - 3)
This equation will give you the plant's height (y) at any given time (x) in months.