How do you determine the equation of a line passing through (2, -3) that is perpendicular to the #4x-y=22#?
To determine this perpendicular line we can use the point-slope formula. We already have a point (2, -3), now we need to determine the slope. The slope of a perpendicular line is the negative inverse of the line it is perpendicular to. If we convert the equation we are given to the slope-intercept form we will have a slope we can take the negative inverse of.
The slope-intercept form is
Given a slope
For our slope of
Now we can use this slope and the point we were given and use the point-slope formula to find the equation of the perpendicular line.
The point-slope formula states:
Substituting the information we have gives:
If we want to convert to the more standard slope-intercept form we would get: