Question

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

Answer 1

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

Explanation: We are given a point and an equation (in standard 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 unknown line we must find, first change the equation we are given from standard form into slope-intercept form. In order to do this, subtract x from both sides of the given equation. This gives us the equation y = -x - 1.

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

So, now that we have the slope of the unknown equation, this is where the given point comes in. This given point lies on the line of the unknown equation. This means that we can plug the slope of the unknown equation and the given point (which lies on the unknown 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 m(the slope), 2 for y1, and 5 for x1. This gives us the equation $y-2=-1(x-5)$. The unknown equation is now known. 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 y by itself. In order to do this, add 2 to both sides of the equation. This gives us $y= -x+7$, which is the answer.

Hope this helps! Have a great day!

-Show work-

Given equation

$x+y=-1$

$x-x+y=-x-1$

$y = -x-1$

Unknown equation:

$y-y_1=m(x-x_1)$

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

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

$y-2=-x+5$

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

$y=-x + 7$