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victus00 [196]
3 years ago
9

Write the equation of the passing line passing through the point (5,2) and parallel of the line x+y= -1

Geography
1 answer:
nlexa [21]3 years ago
6 0

Answer: The equation is [y = -x +7]

Explanation: We are given a point and an equation (in <em>standard </em>form), and are told to find the equation of a line that is parallel to the equation given, and that contains the point given. Before we can even find the equation of the <em>unknown </em>line we must find, first change the equation we are <em>given </em>from <em>standard </em>form into <em>slope-intercept</em> form. In order to do this, subtract <em>x </em>from both sides of the <em>given </em>equation. This gives us the equation<em> y = -x - 1</em>.

Now that we have the <em>given </em>equation in <em>slope-intercept</em> form, we now know that the slope of the <em>given </em>equation is <em>-1</em>. The <em>unknown </em>equation contains a slope that is <em>parallel </em>to the slope of the <em>given </em>equation. This means that the slope of the <em>unknown</em> equation is <em>-1 as well</em>. Still with me so far? Good. It get's a little more complicated from here.

So, now that we have the slope of the <em>unknown</em> equation, this is where the given point comes in. This given point lies on the line of the <em>unknown </em>equation. This means that we can plug the slope of the <em>unknown </em>equation and the given point (which lies on the <em>unknown </em>equation) into point-slope form. Since the formula for the point-slope form is y-y_1=m(x-x_1), we plug in -1 for <em>m</em>(the slope), 2 for <em>y1</em>, and 5 for <em>x1</em>. This gives us the equation y-2=-1(x-5). The <em>unknown </em>equation is now <em>known</em>. All that's left is to change this equation from point-slope form into slope-intercept form.

The first step is to distribute the slope. This changes our equation into y - 2=-x+5. The next step is to get <em>y</em> by itself. In order to do this, add <em>2 </em>to both sides of the equation. This gives us y= -x+7, which is the answer.

Hope this helps! Have a great day!

<h3>-Show work-</h3>

Given equation

x+y=-1

x-x+y=-x-1

y = -x-1

Unknown equation:

y-y_1=m(x-x_1)

y-2=-1(x-5)

y-2=-1(x) + -1(-5)

y-2=-x+5

y-2+2=-x+5+2

y=-x + 7

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