Mathematics, 03.06.2020 14:05 shambrayperkins

Find an equation for the line perpendicular to the line 3x+2y=−1 3x+2y=−1 having the same y-intercept as 2x+7y=2

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Answer from: love6155

The general form for the equation of a line is:

y = mx + c

Where:

m is the gradient of the line

c is the y intercept of the line (y - intercept is where the graph crosses the y-axis)

So if you had the following equation:

y = 3x + 2

Then:

m = 3

c = 2

So gradient = 3, and y intercept = 2

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

Rearranging

So first rearrange both of the equations in the form y = mx + c :

3x + 2y = -1 becomes $y = -\frac{3}{2} x-\frac{1}{2}$ $(where: \ m = -\frac{3}{2} \ and, \ c = -\frac{1}{2} )$

and:

2x+7y=2 becomes $y=-\frac{2}{7}x +\frac{2}{7}$ $(where: \ m = -\frac{2}{7} \ and, \ c = \frac{2}{7})$

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The question tells us that the equation of the line we are looking for has the same y-intercept as:

2x+7y=2

So the line we are trying to work out will also have a y intercept of $\frac{2}{7}$

(refer to rearranging)

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

The question also tells us that the line is perpendicular to 3x + 2y = -1

Perpendicular gradient = negative reciprocal of the gradient of the line it is perpendicular to.

So the gradient of the new line will be the negative reciprocal of the gradient of 3x + 2y = -1

Gradient of 3x + 2y = -1 is: $-\frac{3}{2}$

(refer to rearranging)

Gradient of new line: = negative reciprocal of $-\frac{3}{2}$ , which is $\frac{2}{3}$

(just flip fraction and change the sign)

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

So for the new line: $m = \frac{2}{3} \ and, \ c = \frac{2}{7}$

So just substitute in the values for m and c into: y = mx + c

$y = mx + c\\y = \frac{2}{3} x + \frac{2}{7}$

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So equation of the new line is:

$y = \frac{2}{3}x + \frac{2}{7}$

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Any questions, just ask.

Answer from: Quest

{x = -1/2 , y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer: {x = -1/2 , y = -1

Answer from: Quest

Ineed show the photo because i need more information

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Find an equation for the line perpendicular to the line 3x+2y=−1 3x+2y=−1 having the same y-intercep...