The table shows the height above the ground of a helicopter taking off from the top of a building. What equation in point-slope form gives the
helicopter’s height at any time?
a. y − 9 =3/2(x − 3)
b. y − 9 = 3(x − 3)
c. y + 9 = 3(x + 3)
d. y + 9 =3/2(x + 3)
Table:
3|9
5|15
7|21
9|27
I think it's C but please please please correct me if im wrong ^^"
Update, it was indeed C!! :D
your answer will be y+9=3(x+3)
Lorna your answer is correct its C
Well, let me entertain you with some humor before giving you the correct answer.
Why did the helicopter go to the comedy club?
Because it wanted to take off with a good sense of humor!
Now, getting back to the question, the equation in point-slope form represents a linear relationship between two variables: time (x) and the helicopter's height (y). In point-slope form, the equation is given by y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Let's take the first point (3, 9) from the table and substitute it into the equation options:
a. 9 - 9 = (3/2)(3 - 3) -> 0 = 0, not the correct equation.
b. 9 - 9 = 3(3 - 3) -> 0 = 0, not the correct equation.
c. 9 + 9 = 3(3 + 3) -> 18 = 18, not the correct equation.
d. 9 + 9 = (3/2)(3 + 3) -> 18 = 18, a match!
So, the correct equation in point-slope form is: y + 9 = 3/2(x + 3), option (d).
Hope this helps! Don't hesitate to ask if you have any more questions or need more humor!
To determine the equation in point-slope form that represents the helicopter's height at any time, we must first find the slope.
The slope can be found by taking the difference in height (y-values) and dividing it by the difference in time (x-values).
Using the given data from the table:
(3, 9) and (5, 15), the difference in height is 15 - 9 = 6, and the difference in time is 5 - 3 = 2.
Therefore, the slope is 6/2 = 3.
Next, we choose one of the points, let's say (3, 9), and substitute it into the point-slope equation:
(y - y1) = m(x - x1), where m is the slope, and (x1, y1) represents one of the points.
Substituting the values, we get:
(y - 9) = 3(x - 3), which can be rearranged to y - 9 = 3x - 9.
Simplifying, we get the equation:
y - 9 = 3x - 9.
This equation matches option b, so the correct answer is:
b. y − 9 = 3(x − 3)
To find the equation in point-slope form that gives the helicopter's height at any time, we need to determine the slope and a point on the line.
First, let's find the slope (rise over run) using two points from the table. Let's choose the points (3, 9) and (5, 15) since they have a simple pattern:
slope = (change in y) / (change in x)
= (15 - 9) / (5 - 3)
= 6 / 2
= 3
Now that we have the slope, we can write the equation in point-slope form using any point on the line. Let's use the point (3, 9):
y - y₁ = m(x - x₁) -- Point-Slope Form
Replacing y₁ with 9, x₁ with 3, and m with 3, the equation becomes:
y - 9 = 3(x - 3)
Thus, the equation in point-slope form that gives the helicopter's height at any time is:
y - 9 = 3(x - 3)
Therefore, your answer is correct. It is option a. y - 9 = 3/2(x - 3).