The table shows the height of a plant as it grows. Which equation in plot-slop form gives the plants height at any time
3|21
5|35
7|49
9|63
answers-
y-21=7/2(x-3)
y-21=7(x-3)
y-3=7/2(x-21)
the relationship is nonlinear
2nd one
Well, well, looks like we have a height-chart for our plant! It's growing up so fast! Now, let's figure out the equation that describes its growth.
Alright, let's take a look at the options we have. "y-21=7/2(x-3)" and "y-21=7(x-3)" both seem like possibilities. But which one fits the bill?
If we look at the points on the table, we can see that as the x-values increase by 2, the y-values increase by 14. This means that for every 2 units increase in x, there's a 14 units increase in y.
Now, let's see if "y-21=7/2(x-3)" aligns with our observations. If we plug in the values for x and y from the table, we'll find that "y-21=7/2(x-3)" does satisfy the growth pattern we see.
Therefore, the equation in slope-intercept form that gives the plant's height at any time is "y-21=7/2(x-3)".
Now, let's celebrate the growth of our little green friend! 🌱🎉
To find the equation in point-slope form that represents the relationship between the time (x) and the plant's height (y), we need to determine the slope (m) and the y-intercept (b) using the given data points:
Point 1: (3, 21)
Point 2: (5, 35)
Point 3: (7, 49)
Point 4: (9, 63)
First, let's find the slope (m) using two points (3, 21) and (5, 35):
m = (y2 - y1) / (x2 - x1)
m = (35 - 21) / (5 - 3)
m = 14 / 2
m = 7
Next, let's determine the y-intercept (b) by substituting one of the points in the slope-intercept form of a linear equation (y = mx + b) and solving for b. Let's use point (3, 21):
21 = 7(3) + b
21 = 21 + b
b = 0
Now we have the slope (m) and y-intercept (b), and we can write the equation in slope-intercept form:
y = mx + b
y = 7x + 0
y = 7x
Therefore, the correct equation in slope-intercept form that gives the plant's height at any time is: y = 7x.
To determine which equation in slope-intercept form gives the plant's height at any time, we need to find the slope. The slope represents the rate at which the plant's height is changing over time.
First, let's calculate the slope using the given data points. We can select any two points from the table. Let's choose (3, 21) and (9, 63) to calculate the slope of the plant's growth:
slope = (change in y) / (change in x)
= (63 - 21) / (9 - 3)
= 42 / 6
= 7
The slope gives us the rate at which the plant's height is increasing. Now, we can use this slope and one of the points to find the equation in slope-intercept form. Let's choose the point (3, 21):
y - y1 = m(x - x1)
y - 21 = 7(x - 3)
Therefore, the correct equation in slope-intercept form that gives the plant's height at any time is:
y - 21 = 7(x - 3)
Out of the given options, the equation that matches this form is:
y - 21 = 7(x - 3)
So, the answer is:
y - 21 = 7(x - 3)