Find the equation of a line perpendicular to y=-x-1 that passes through the point (2,9)

To find the equation of a line perpendicular to $y=-x-1$ that passes through the point $(2,9)$, we need to determine the slope of the perpendicular line.<br /><br />The slope of the given line $y=-x-1$ is $-1$. The slope of a line perpendicular to this line is the negative reciprocal of $-1$, which is $1$.<br /><br />Now, we can use the point-slope form of a linear equation to find the equation of the perpendicular line. The point-slope form is given by:<br /><br />$y - y_1 = m(x - x_1)$<br /><br />where $(x_1, y_1)$ is a point on the line and $m$ is the slope.<br /><br />Substituting the given point $(2,9)$ and the slope $m=1$ into the equation, we have:<br /><br />$y - 9 = 1(x - 2)$<br /><br />Simplifying this equation, we get:<br /><br />$y - 9 = x - 2$<br /><br />$y = x + 7$<br /><br />Therefore, the equation of the line perpendicular to $y=-x-1$ that passes through the point $(2,9)$ is $y = x + 7$.