The equation of the line l is $5 + y - 2x = 0$ - Junior Cycle Mathematics - Question 6 - 2015

To find the slope, we can rewrite the equation in the slope-intercept form $y = mx + b$.
Starting from the equation:

$5 + y - 2x = 0$
Rearranging gives:
$y = 2x - 5$

The slope (m) is the coefficient of x, which is 2. Therefore, the slope of line l is 2.

Since line j is perpendicular to line l, we take the negative reciprocal of the slope of l.
The slope of line l is 2, so the slope of line j, denoted as $m_j$, is:
$m_j = -\frac{1}{2}.$

We can use the point-slope form of the line equation to find the equation of line j. The point (11, 6) and the slope $m_j = -\frac{1}{2}$ are given.
The point-slope form is:
$y - y_1 = m(x - x_1)$
Substituting the values, we get:
$y - 6 = -\frac{1}{2}(x - 11)$
Simplifying this, we multiply through by -2 to eliminate the fraction:

$-2(y - 6) = (x - 11)$

Expanding gives:
$-2y + 12 = x - 11$

Rearranging it into standard form results in:
$x + 2y - 23 = 0.$
Therefore, the equation of line j is x + 2y - 23 = 0.