Evaluate the expression 5^2+10.2×4-2

3.1 Find the equation of the line passing through (4, 5) and parallel to the line 3x – 2y = 4.

valentinak56 [21]

$\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}$

<em>Find the equation of the line passing through (4, 5) and parallel to </em>

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<em> </em> $\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}$

First of all, We need to convert this equation from standard form (ax+by=c) into slope-intercept form (y=mx+b).

$\rightarrow$ First, add 2y on both sides:-

$\Large\textsf{3x+2y=4}$

$\rightarrow$ Now, subtract 3x on both sides:-

$\Large\textsf{2y=-3x+4}$

$\rightarrow$ Divide by 2 on both sides

$\Large\text{$y=-\displaystyle\frac{3}{2}x +2$}$

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Now, let's find the equation of the line that's parallel to the given line.

Remember, if lines are parallel to each other, then their slope's the same.

So the slope of the line that's parallel to the line whose equation we just found, is

$\Large\text{$-\displaystyle\frac{3}{2}$}$

Now let's write the equation in point-slope form:-

$\hookrightarrow\sf{y-y_1=m(x-x_1)}$

Replace numbers with letters, as follows:-

$\sf{y-5=-\displaystyle\frac{3}{2} (x-4)}$

The equation above is the equation in point-slope form.

Incase you need it converted to slope intercept form, refer to the steps below ~

Multiply -3/2 times x and -4:-

$\hookrightarrow\sf{y-5=-\displaystyle\frac{3}{2} x-6}$

Now, Add 5 on both sides:-

$\hookrightarrow\sf{y=\displaystyle\frac{3}{2} x+1}$

$\Uparrow\sf{Our\:equation\:in\:slope\;intercept\;form}$

<h3>Good luck with your studies.</h3>

#TogetherWeGoFar

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4 0

2 years ago

Explain why the slope of line a is 2/6.

kifflom [539]

Answer:

The slope of a line is 2/6 because slope also means rise over run (y/x). So the line's slope is 2/6 because it goes up (rises) in the y-direction 2 units and moves to the right (runs) 6 units, from one point to another.

Step-by-step explanation:

5 0

3 years ago

Mr. Marcus is splitting a huge new pack of colored pencils equally among his 25 students. After splitting the pencils he has 4 l

mamaluj [8]

Answer:

Each student got 17 pencils

Step-by-step explanation:

(429-5)/25=x

3 0

4 years ago

4. Six workers are hired to weed a field by

user100 [1]

Answer:

594 square feet

Step-by-step explanation:

Area of a rectangle is length times width. We can find the area of each workers plot by multiplying 9 and 11 to get 99 sq feet. There is six workers, and therefore six plots of land, so we'd take our 99 sq feet and count that six times to get 594 square feet.

4 0

3 years ago

Find an expression which represents the difference when (6x-3y) is subtracted from (9x+2y) in simplest terms.

Alex73 [517]

Answer:

$3x+5y$