Question

PLEASE HELP ME I DONT UNDERSTAND GIVING 100 POINTS

Question 1: The Magnolia trees purchased for planting at the school are 3 feet tall. Research shows that these types of trees grow at an average of 3/4 foot per year

Some students misunderstood question #1 and wrote the following equations in point-slope form:
a) y − 3 = 3/4(x-0)
b) y - 6 = 3/4(x-4)
c) y - 4.5 = 3/4(x-2)
d) y - 12 = 3/4(x-12)
(e) y - 15= 3/4(x-15)

Is this equation okay to use for the height of the trees in this problem?

There is one equation that is incorrect.... determine which one? why is it incorrectly?

Creat two new equations written in point slope form

Answer 1

• (e) is the incorrect equation

• y -9 = 3/4(x -8)
• y -15 = 3/4(x -16)

Explanation:

Given a tree is 3 ft tall when planted and grows at 3/4 ft per year, you want to identify the point-slope equation that does NOT fit this description, and you want two (2) more point-slope equations that DO fit this description.

Point-slope equation

The point-slope equation of a line with slope m through point (h, k) is ...

y -k = m(x -h)

Points

The point representing the initial height of the tree is (x, y) = (years, feet) = (0, 3). If the rate of growth is 3/4 ft per year, then the equation can be written ...

y -3 = 3/4(x -0) . . . . . . . . . matches choice (a)

All of the given equations have m = 3/4, so to find the incorrect equation, we need to find the point that is not on the line described by the above equation. We can do this by identifying the point (h, k) in each equation.

The attachment shows the point values used in each of the other equations (b) through (e). We find they all fall on the line except the point (15, 15) used in equation (e).

The incorrect equation is equation (e) y -15 = 3/4(x -15).

Additional equations

We can write additional equations by finding additional points that are on the line. For the purpose, it is convenient to choose x-values that are multiples of 4. Already, equations use x = 0, 4, 12, 15. We can choose x=8 and x=16 for the equations we write. The graph shows the corresponding y-values are 9 and 15, respectively. Then two additional equations could be ...

y -9 = 3/4(x -8)

y -15 = 3/4(x -16)

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Additional comment

There are several ways to find the equation that doesn't belong. Another way, apart from plotting the points on a graph, is to rewrite each equation into the same form. Slope-intercept form is fairly convenient for this.

(a) y -3 = 3/4(x -0) ⇒ y = 3/4x +3

(d) y -12 = 3/4(x -12) ⇒ y = 3/4x -9 +12 = 3/4x +3

(e) y -15 = 3/4(x -15) ⇒ y = 3/4x -11.25 +15 = 3/4x +3.75 (incorrect)

You can see that 3/4x (and y) will be an integer only if x is a multiple of 4. We like integers, so it is convenient to choose x as a multiple of 4.

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