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3 years ago

Write the equation of a line passing through (2, 1) that is parallel to the line passing through (-1,2) and (0, -1)

1 answer:

8 0

y = -3x + 7 is the equation of a line passing through (2, 1) that is parallel to the line passing through (-1,2) and (0, -1)

Solution:

Given that, we have to write the equation of a line passing through (2, 1) that is parallel to the line passing through (-1,2) and (0, -1)

Find the slope of line

The slope of line is given by formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

Here given that line is parallel to the line passing through (-1, 2) and (0, -1)

Therefore,

$(x_1, y_1) = (-1, 2)\\\\(x_2, y_2) = (0, -1)$

Substituting the values we get,

$m = \frac{-1-2}{0-(-1)}\\\\m = \frac{-3}{1}\\\\m = -3$

Thus slope of line is -3

We know that, slopes of parallel lines are equal

Therefore, slope of line parallel to the line passing through (-1,2) and (0, -1) is also -3

Now find the equation of line with slope -3 and passing through (2, 1)

The equation of line in slope intercept form is given as:

y = mx + c ------ eqn 1

Where, "m" is the slope of line and "c" is the y intercept

Substitute m = -3 and (x, y) = (2, 1) in eqn 1

1 = -3(2) + c

1 = -6 + c

c = 7

Substitute m = -3 and c = 7 in eqn 1

y = -3x + 7

Thus the equation of line is found

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Answer:

Option A) $\angle F\\$ congruent with $\angle Q$

Step-by-step explanation:

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3 years ago

In 2000, Canada produced 3.0 million new motor vehicles. In 2006, it produced 2.5 million. Write the linear equation (in slope-i

kogti [31]

To begin, you are given two point that this function would intercept: (0,3) where the 0 is the original year (2000) and 3 is the amount of million cars sold. The next point would be (6,2.5) Where the 6 is the 6 years later and the 2.5 is the 2.5 million cars sold. Since we have 2 points, we can work out the gradient by finding the rate of change in y and dividing by the rate of change in x:
$\frac{y_{1}- y_{2} }{x_{1}- x_{2} }$

We then substitute in the points:
$x_{1} =3$
$y_{1} =0$
$x_{2} =2.5$
$y_{2} =6$

$\frac{3-2.5}{0-6}$
$=\frac{0.5}{-6}$
$=-.083$

Because we started on the y-intercept of (0,3), we already have our intercept value of 3. If we did not start with the y-intercept given, we could substitute in a point to solve for it:

Using point (2.5,6):

 $2.5=-0.083*6+c$
 $2.5=-0.5+c$
$2.5+0.5=c$
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Hope this helps :)

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3 years ago

Which is the same as moving the decimal point 3 places to the left in a decimal number?

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4 years ago

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In a florist shop, the ratio of roses to tulips is 5 : 3. The shop has 72 tulips on Friday morning. If the florist uses up half

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3 years ago

Explain how to use Pascal's Triangle to expand the binomial (3x-4y)^11

Mars2501 [29]

The solution to the binomial expression by using Pascal's triangle is:

$\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}$

$\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}$

$\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}$

<h3>How can we use Pascal's triangle to expand a binomial expression?</h3>

Pascal's triangle can be used to calculate the coefficients of the expansion of (a+b)ⁿ by taking the exponent (n) and adding the value of 1 to it. The coefficients will correspond with the line (n+1) of the triangle.

We can have the Pascal tree triangle expressed as follows:

1 1

1 2 1

1 3 3 1

1 4 6 4 1

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

From the given information:

The expansion of (3x-4y)^11 will correspond to line 11.

Using the general formula for the Pascal triangle:

$\mathbf{(a+b)^n = c_oa^nb^0 + c_1 a^{n-1}b^1+c_{n-1}a^1b^{n-1}+c_na^0b^n}$

The solution to the expansion of the binomial (3x-4y)^11 can be computed as:

$\mathbf{=177147x^{11}-2598156x^{10}y +17321040x^9y^2-69284160x^8y^3+184757760x^7y^4}$

$\mathbf{-344881152x^6y^5+459841536x^5y^6-437944320x^4y^7+291962880x^3y^8}$

$\mathbf{-129761280x2y^9+34603008xy^{10}-4194304y^{11}}$

Learn more about Pascal's triangle here:

brainly.com/question/16978014

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