Write the equation of the line passing through (- 1, 4) ) and perpendicular to x + 2y = 11

y = x + 5

Step-by-step explanation:

The slope of the given line x + 2y = 11 is found as follows:  Solve x + 2y = 11 for 2y first, and then for y.  The slope is then the coefficient of the x term:

2y = 11 -x  =>  y = -x + 11.  The slope is thus m = -1.

The slope of any line perpendicular to y = -x + 11 is the negative reciprocal of -1, which is -(-1), or +1.

Thus, the desired line has slope 1 and passes through (-1, 4):

y = mx + b becomes

4 = 1(-1) + b, or b = 5.

Thus, the desired equation is    y = x + 5.