Answer:
Y= x - 1
Explanation:
To find the equation of a line that is parallel to the line x - y = 9 and passes through the point (-1, -2), we need to determine the slope of the given line.
The equation x - y = 9 can be rearranged to y = x - 9 by adding y to both sides. This equation is in slope-intercept form (y = mx + b), where m represents the slope of the line. In this case, the slope is 1.
Since parallel lines have the same slope, the line we are looking for will also have a slope of 1.
Now that we know the slope and have a point on the line (-1, -2), we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1),
where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have:
y - (-2) = 1(x - (-1)),
Simplifying further, we get:
y + 2 = x + 1.
To write this equation in the standard slope-intercept form (y = mx + b), we can subtract 2 from both sides:
y = x - 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.