Find an equation of the line that passes through (5,7) and is perpendicular to y=5x-4.

Question

The concept of the equation.

Answer 1

The graph of y = mx + b is a line with slope m and y-intercept (0, b).  So, y = 5x - 4 has slope 5.  

 

The slopes of perpendicular lines are negative reciprocals. Therefore, any line perpendicular to the line with equation                 

y = 5x - 4 has slope -1/5.

 

Using the point-slope form for the equation of a line, an equation of the line with slope -1/5 and which goes through the point (5,7) is:

 

y - 7 = (-1/5)(x - 5)

 

y - 7 = (-1/5)x + 1

 

y = (-1/5)x + 8