How do you write an equation of a line that contains the given point (-5,5) and is perpendicular to the given line y=-5x+9?
To find the equation of the line perpendicular to the given line and going through the given point we will use the point-slope formula. We have been given a point so what we are missing is the slope.
The given line is in slope-intercept form.
The slope-intercept form of a linear equation is:
Therefore we know the slope of the given line,
A perpendicular line will have a slope which is the negative inverse of this line, or
We can now use the point-slope formula to write the equation for the perpendicular line.
The point-slope formula states:
Substituting the point we were given and the slope we calculated gives:
or, we can solve for