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Masja [62]
3 years ago
5

What equation represents the line that passes through (-8,11) and (4,7/2)

Mathematics
2 answers:
masha68 [24]3 years ago
8 0

For this case we have that by definition, the equation of the line in slope-intersection form is given by:

y = mx + b

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We have:

(x1, y1): (- 8,11)\\(x2, y2): (4,3.5)

m = \frac {y2-y1} {x2-x1} = \frac {3.5-11} {4 - (- 8)} = \frac {-7.5} {4 + 8} = \frac {-7.5} {12 } = - \frac {\frac {15} {2}} {12} = - \frac {15} {24} = - \frac {5} {8}

Thus, the equation will be given by:

y = - \frac {5} {8} x + b

We substitute a point to find "b":

11 = - \frac {5} {8} (- 8) + b\\11 = 5 + b\\b = 11-5\\b = 6

Finally:

y = - \frac {5} {8} x + 6

Answer:

y = - \frac {5} {8} x + 6

Marianna [84]3 years ago
4 0

Answer:

So our answers could be any of these depending on the form wanted*:

y=\frac{-5}{8}x+6

5x+8y=48

y-11=\frac{-5}{8}(x+8)

y-\frac{7}{2}=\frac{-5}{8}(x-4)

*There are other ways to write this equation.

Step-by-step explanation:

So we are given two points on a line: (-8,11) and (4,7/2).

We can find the slope by using the formula \frac{y_2-y_1}{x_2-x_1} \text{ where } (x_1,y_1) \text{ and } (x_2,y+2) \text{ is on the line}.

So to do this, I'm going to line up my points vertically and then subtract vertically, then put 2nd difference over 1st difference:

( 4  ,  7/2)

-(-8 ,    11)

----------------

12      -7.5

So the slope is -7.5/12 or -0.625 (If you type -7.5 division sign 12 in your calculator).

-0.625 as a fraction is -5/8 (just use the f<->d button to have your calculator convert your decimal to a fraction).

Anyways the equation of a line in slope-intercept form is y=mx+b where m is the slope and b is y-intercept.

We have m=-5/8 since that is the slope.

So plugging this into y=mx+b gives us y=(-5/8)x+b.

So now we need to find b. Pick one of the points given to you (just one).

Plug it into y=(-5/8)x+b and solve for b.

y=(-5/8)x   +b with (-8,11)

11=(-5/8)(-8)+b

11=5+b

11-5=b

6=b

So the equation of the line in slope-intercept form is y=(-5/8)x+6.

We can also put in standard form which is ax+by=c where a,b,c are integers.

y=(-5/8)x+6

First step: We want to get rid of the fraction by multiplying both sides by 8:

8y=-5x+48

Second step: Add 5x on both sides:

5x+8y=48 (This is standard form.)

Now you can also out the line point-slope form, y-y_1=m(x-x_1) \text{ where } m \text{ is the slope and } (x_1,y_1) \text{ is a point on the line }

So you can say either is correct:

y-11=\frac{-5}{8}(x-(-8))

or after simplifying:

y-11=\frac{-5}{8}(x+8)

Someone might have decided to use the other point; that is fine:

y-\frac{7}{2}=\frac{-5}{8}(x-4)

So our answers could be any of these depending on the form wanted*:

y=\frac{-5}{8}x+6

5x+8y=48

y-11=\frac{-5}{8}(x+8)

y-\frac{7}{2}=\frac{-5}{8}(x-4)

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Q3: x = 4, y = 4, z = 4

Q4: x = 6, y = 0, z = -4

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Since all three equations have a z in them, I will first solve for z.

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Rearrange them so that the letters are on one side and numbers on the other side.

First equation: y + 6z = -24

Second equation: z + 2y = -4

I will choose to eliminate the y (You can choose either or)

Multiply the first equation by 2

2(y + 6z = -24)

2y + 12z = -48

Now that 2y is in both equations, we can minus one equation from the other to eliminate the y (I will minus the second from the first)

First Eq: 2y + 12z = -48

Second Eq: z + 2y = -4

2y - 2y = 0y

12z - z = 11z

-48 - (-4) = -44

Type these answers into a new equation

0y + 11z = - 44

Since y is 0, ignore it. Solve for z

11z = -44

z = -44/11

z = - 4

Substitute our z into either the first or second equation and solve for y (It doesnt matter which one you choose, I just did the second equation)

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(-4) + 2y = -4

2y = -4 + 4

2y = 0

y = 0

Substitute in our y and z values into the third equation and solve for x

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-6x - 6(0) - 6(-4) = -12

-6x - 0 + 24 = -12

-6x = -12 - 24

-6x = -36

x = -36/-6

x = 6

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