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3 years ago

Write in slope-intercept form of the equation of the line through the given point. Through: (-3,-3) and (4,0)

Mathematics

2 answers:

adoni [48]3 years ago

6 0

Answer:

y = 3/7 x - 12/7

Step-by-step explanation:

The slope is (0+3)/(4+3) = 3/7

So, now you have a point and a slope, so use the point-slope form. That gives you

y-0 = 3/7 (x-4)

Now just rearrange to slope-intercept form.

y = 3/7 x - 12/7

Eduardwww [97]3 years ago

4 0

You have to use the y2-y1 over x2-x1.
So, let's plug the numbers in.
(-3,-3)
^ ^
X1 Y1
(4,0)
^ ^
X2 Y2
So, that would be
0-(-3)
——
4-(-3)
The two subtraction signs counteract and become a positive, or addition symbol. So it would be
0+3
——
4+ 3
Do the addition to get 3 over 7 or
3
—
7

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A line passes through the points (-3, 5) and (2, 3). What is the slope of this line

vfiekz [6]

Answer:

slope is -2/5

Step-by-step explanation:

m=y2-y1/x2-x1

m=3-5/2-(-3))

m=-2/2+3

m=-2/5

8 0

2 years ago

Solve y'' + 10y' + 25y = 0, y(0) = -2, y'(0) = 11 y(t) = Preview

svetlana [45]

Answer: The required solution is

$y=(-2+t)e^{-5t}.$

Step-by-step explanation: We are given to solve the following differential equation :

$y^{\prime\prime}+10y^\prime+25y=0,~~~~~~~y(0)=-2,~~y^\prime(0)=11~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$y=e^{mt}$ be an auxiliary solution of equation (i).

Then, we have

$y^prime=me^{mt},~~~~~y^{\prime\prime}=m^2e^{mt}.$

Substituting these values in equation (i), we get

$m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.$

So, the general solution of the given equation is

$y(t)=(A+Bt)e^{-5t}.$

Differentiating with respect to t, we get

$y^\prime(t)=-5e^{-5t}(A+Bt)+Be^{-5t}.$

According to the given conditions, we have

$y(0)=-2\\\\\Rightarrow A=-2$

and

$y^\prime(0)=11\\\\\Rightarrow -5(A+B\times0)+B=11\\\\\Rightarrow -5A+B=11\\\\\Rightarrow (-5)\times(-2)+B=11\\\\\Rightarrow 10+B=11\\\\\Rightarrow B=11-10\\\\\Rightarrow B=1.$