Problem:
Write the equation of a line perpendicular to y=-1/3x-10 that passes through (-1,5).
Solution:
By definition, the slope-intercept equation of a line is given by the following formula:
where m is the slope of the line and b is the y-coordinate of the y-intercept. Now, if we have the equation of a line, given by the formula:
then, the slope of this line is -1/3. Now, perpendicular lines have slopes that are the opposite of the reciprocal of each other. In this case, if the slope of the first line is -1/3, the reciprocal of -1/3 is -3, so the opposite of the reciprocal is, therefore 3. Then, the slope of the line perpendicular to y=-1/3x-10 is m = 3, and its equation would be:
y = -3x +b
now, to find b, we take any point of the above line and replace it in the above equation. Take for example, (x,y) = (-1,5), then we have:
5 = -3(-1) + b
this is equivalent to:
5 = 3 + b
solving for b, we get:
b = 2.
then, we can conclude that the equation of a line perpendicular to y=-1/3x-10 that passes through (-1,5) is
