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IgorLugansk [536]
3 years ago
14

Write an equation of each line that passes through the following points in slope-intercept form:

Mathematics
1 answer:
sdas [7]3 years ago
5 0

Answer:

1.  y = -3/2 x +11

2.  y = -2 x -7

Step-by-step explanation:

Slope intercept form is y = mx+b

1. A (8, –1) and B (–4, 17)

First we need to find the slope

m = (y2-y1)/(x2-x1)

m = (17--1)/(-4-8)

   =(17+1)/(-4-8)

   =18/-12

Dividing top and bottom by 6

  =-3/2

Given the slope

y = -3/2 x+b

Using the point (8,1) we can find b

-1 = -3/2(8) +b

-1 =-12 +b

Add 12 to each side

-1+12 = -12+12 +b

11 =b

The equation is y = -3/2 x +11

2. C (–19, 31) and D (1, –9)

First we need to find the slope

m = (y2-y1)/(x2-x1)

m = (-9-31)/(1--19)

   =(-40)/(1+19)

   = -40/20

   =-2

Given the slope

y = -2 x+b

Using the point (1,-9) we can find b

-9 = -2(1) +b

-9 =-2 +b

Add 2 to each side

-9+2 = -2+2 +b

-7 =b

The equation is y = -2 x -7

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Answer:

The ball will reach the same height of 10 meters after 100 meters.

Part A)

100 meters.

Part B)

10 meters.

Step-by-step explanation:

The golf-ball hit by the Seven-Iron is modeled by the equation:

h=-0.002d^2+0.3d

And the ball hit by the Nine-Iron is modeled by the equation:

h=-0.004d^2+0.5d

Where <em>h</em> is the height of the ball after <em>d</em> meters.

When they are at the same height, the two equations will equal each other.

Graphically, this is where the two graphs will intersect.

To solve this using a Ti-84, you can follow these steps (I'm using the Ti-84 Plus Silver Edition):

1) Using [Y=], write and then [GRAPH] the two equations.

2) Press [ZOOM] and [ZOOM OUT] until you can see both graphs clearly.

3) To find the intersection point, press [2ND] and then [CALC] (above [TRACE]).

4) Choose [5) Intersect].

5) Using the arrow keys, click on one graph to choose it as your first curve and the other to choose it as your second curve. (In this case, it doesn't matter which one is which.)

6) When it asks you to guess, put the cursor to as close to the intersection point as possible. Ignore the intersection at the origin point.

7) Press [ENTER], and it should give you your solution.

Therefore, the intersection point (not counting (0,0)) is at (100, 10).

Therefore, the ball will reach the same height of 10 meters after 100 meters.

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