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) Height (inches) 2 14 4 23 6 32 8 41
To find the equation in slope-intercept form, we need to determine the slope and y-intercept.
Let's first find the slope by using two points from the table. We can choose the first and second points, (2, 14) and (4, 23).
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (2, 14) and (4, 23):
m = (23 - 14) / (4 - 2)
m = 9 / 2
m = 4.5
Now, let's find the y-intercept (b) by using one point on the line. We can choose any point from the table. Let's choose (2, 14).
The equation in slope-intercept form is given by:
y = mx + b, where m is the slope and b is the y-intercept.
Using the point (2, 14):
14 = 4.5(2) + b
14 = 9 + b
b = 14 - 9
b = 5
Therefore, the equation in slope-intercept form that gives the tree's height at any time is:
y = 4.5x + 5, where x represents the time in months and y represents the height in inches.
are you sure
Yes, I am confident in the equation provided. It is derived from the given data points and follows the slope-intercept form of a linear equation, with the slope representing the rate of change in height over time and the y-intercept representing the initial height of the tree.
it is not a choice
I apologize for the confusion. Since you mentioned it is a multiple-choice question, could you please provide the options? That way, I can help you choose the correct equation for the tree's height.
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) Height (inches) 2 14 4 23 6 32 8 41 (1 point) Responses y = 9x + 2 y = 9 x + 2 y = x + 5 y = Image with alt text: start fraction 9 over 2 end fraction x + 5 y = x y = Image with alt text: start fraction 9 over 2 end fraction x y = 5x +
To determine the equation in slope-intercept form, we can first calculate the slope using two points from the table. Let's use the first and second points, (2, 14) and (4, 23).
The slope (m) can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (2, 14) and (4, 23):
m = (23 - 14) / (4 - 2)
m = 9 / 2
m = 4.5
Next, we can find the y-intercept (b) by using any point from the table. Let's choose (2, 14).
The equation in slope-intercept form is given by:
y = mx + b, where m is the slope and b is the y-intercept.
Using the point (2, 14):
14 = 4.5(2) + b
14 = 9 + b
b = 14 - 9
b = 5
Therefore, the correct equation in slope-intercept form for the tree's height at any time is:
y = 4.5x + 5.
Among the options provided, the correct response would be:
y = 4.5x + 5.