Answer:
The equation of line passing through point (2 , 2) and perpendicular to line y = x is y = - x + 4 .
Step-by-step explanation:
Given as :
The line equation is y = x
Now, equation of line in slope-intercept form y = m x + c
where m is the slope of line and c is y-intercept
Comparing given line equation with standard line equation
The slope of line y = x is m = 1
Again
Other line is passing through point (2 ,2) and is perpendicular to line y = x
Let The slope of other line = M
∵ From perpendicular lines property
Product of slope of lines = - 1
i.e m × M = - 1
Or , M = [tex]\dfrac{ - 1}{m}[/tex]
Or, M = [tex]\dfrac{ - 1}{1}[/tex]
∴ M = - 1
Now, Equation of other line in point-slope form
The other line is passing through point (2 , 2) and slope M = - 1
So, y - [tex]y_1[/tex] = M × (x - [tex]x_1[/tex])
Or, y - 2 = - 1 × ( x - 2 )
Or, y - 2 = - x + 2
Or, y = - x + 2 + 2
Or, y = - x + 4
Hence, The equation of line passing through point (2 , 2) and perpendicular to line y = x is y = - x + 4 . Answer
