Answer: An equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:
y = -4x + 20
Explanation:
The given equation is in slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept. The slope of the line is 2, which means the line has a slope of 2 and is inclined at an angle of tan^-1(2).
To find an equation of a line that is perpendicular to this line, we need to find the negative reciprocal of the slope, which is -1/2. This means the slope of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is -1/2.
Now we can use the point-slope form of a linear equation to find the equation of the line passing through point P(-6, 4) and having a slope of -1/2. The point-slope form of a linear equation is:
y - y1 = m(x - x1)
Where (x1, y1) is the given point, and m is the slope of the line. So by substituting the values we get:
y - 4 = -1/2(x + 6)
Which can be written as:
y = -1/2x + 4
So the equation of the line passing through point P(-6, 4) that is perpendicular to y + 8 = 2(x - 14) is:
y = -1/2x + 4
Graphing the equations can confirm that the lines are perpendicular as the slope of the first line is 2 and the slope of the second line is -1/2, the product of these slopes is -1 which means they are perpendicular to each other.