Question

What is an equation of the line that passes through the point (-5,-2) and is

parallel to the line x - y = 5?

Answer 1

`y=x+3`

Explanation:

What we need to know

1. Linear equations are typically organized in slope-intercept form:
   `y=mx+b` where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)
2. Parallel lines have the same slope

1) Rewrite the equation x - y = 5 into slope-intercept form and identify the slope

`x - y = 5`

Subtract both sides by x

`x - y -x= -x+5\\-y= -x+5`

Divide both sides by -1

`y= x-5`

Now, we can tell clearly that the slope (m) of this line is 1. Therefore, a line parallel to this would also have a slope of 1.

Plugging 1 as m into
`y=mx+b`, we get:

`y=x+b`

2) Find the y-intercept (b) of the line parallel to
`y= x-5` and find the final equation

`y=x+b`

Plug in the given point (-5,-2)

`-2=-5+b`

Add 5 to both sides

`-2+5=-5+b+5\\3=b`

Therefore, the y-intercept of this line is 3. Now, plugging this back into our original equation, we get:

`y=x+b\\y=x+3`

I hope this helps!