Answer: The given equation is y + 4 = x - 9, which can be rewritten as y = x - 13 by subtracting 4 from both sides and adding 9 to both sides.
We can see that the slope of this line is 1.
To find an equation representing a different line with the same slope, and passing through the point (3,6), 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.
Substituting the values, we get:
y - 6 = 1(x - 3)
Simplifying, we get:
y - 6 = x - 3
or
y = x + 3
Therefore, the equation of the line with the same slope that passes through the point (3,6) is y = x + 3.
Explanation: