Question 132228This question is from textbook
: What is the equation of the line passing through (-3, 7) and perpendicular to -7x-8y=77? This question is from textbook
You can put this solution on YOUR website! Lines are perpendicular if and only if their slopes are negative reciprocals of each other. If is the slope of one of the lines and is the slope of the other line, then they are perpendicular if .
Start with the equation of the given line and put it into slope-intercept form () by solving for y:
Therefore the slope of the given line is because that is the coefficient on x when the equation is in slope-intercept form.
Since you want to derive the equation for a line perpendicular to the given line, you need the negative reciprocal of the slope of the given line, so:
Now that you have the slope determined and you are given a point, you can use the point-slope form to derive the equation of the desired perpendicular.
Point-slope form: where (,) are the co-ordinates of the given point and m is the slope.
, is an equation for the desired line. However, you probably want to put it into standard form just like the given equation at the start.
