What is an equation of the line that passes through the point left bracket, minus, 1, comma, minus, 2, right bracket(−1,−2) and is parallel to the line x, minus, y, equals, 9x−y=9?

Answer 1

To find the equation of the line that passes through the point (-1,-2) and is parallel to the line x-y=9, we first need to find the slope of the given line.

The equation of the given line is x-y=9, which can be rewritten in slope-intercept form as y=x-9. The slope of the given line is 1.

Since the line we are looking for is parallel to the given line, it will have the same slope. The equation of the line passing through (-1,-2) with slope 1 can be written as:

y = mx + b
y = x + b

Now, substitute the point (-1,-2) into the equation to find the value of b:

-2 = -1 + b
b = -2 + 1
b = -1

So, the equation of the line that passes through the point (-1,-2) and is parallel to the line x-y=9 is:

y = x - 1