A peregrine falcon dives for prey. Its elevation changes

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>

<em />

<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

5.

adell [148]

Answer:

Solving the inequality $3x -2 < 4$ we get $\mathbf{x$

Option D is correct option.

Step-by-step explanation:

We need to solve the inequality $3x -2 < 4$ and find value of x

Solving the inequality for finding value of x, we will keep x on left side of inequality and all other terms on the right side.

$3x -2 < 4$

Adding 2 on both sides

$3x -2+2 < 4+2\\3x < 6$

Now, we will divide 3 on both sides

$\frac{3x}{3}$

So, we get x < 2

Solving the inequality $3x -2 < 4$ we get $\mathbf{x$

Option D is correct option.

5 0

2 years ago

If the first equation in a linear system is 4x - 2y = -2 what would the second equation have to be for the system to have infini

alekssr [168]

Answer:

<h3>The question, </h3>

,

<h3>Let me explain, </h3>

<h3>For infinity many solutions </h3>

They must be parallel to each other,

For instance,

If 4x - 2y = - 2 is the equation then,

<h3>Another equation be 4x - 2y +k = </h3>

Where k can be any numerical value.

<h3 />

7 0

3 years ago

Imagine if adam sandler died:(

charle [14.2K]

This would be horrible my favorite movie is big daddy, it’s a classic. i used to watch with my uncle all the time. it reminds me of him so much

7 0

3 years ago

Read 2 more answers

Same thing I said before and not saying it again, 61 points to whomever can help me out with mathematics. All math questions not

Aliun [14]

Answer:3040

Step-by-step explanation:16000/100=160x19=3040

6 0

3 years ago

Read 2 more answers