First, we know that the x-intercept and y-intercept of the original line are 1 and -2 respectively. The slope of this line is calculated by dividing the y-intercept by the x-intercept, which gives us -2.
Secondly, we note that the slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. So, the perpendicular slope for our given line is -1 divided by -2, which is 0.5.
Now, we are told that the line we want to find the equation for passes through the point (-6,4). To find the equation of a line given a point (x1, y1) that the line passes through and the line's slope, we use the point-slope form of a line, which states that the change in y equals the slope times the change in x, or y - y1 = m(x - x1 ).
To apply the point-slope form to our problem, we substitute the given point (-6,4) into the formula, and use the slope we calculated earlier, getting y - 4 = 0.5(x - (-6)).
Simplifying, we find the equation of the line is y = 0.5(x + 6) + 4.
This is the equation of the line that passes through (-6,4) and is perpendicular to the line that has x-intercept = 1 and y-intercept = -2.