Answer: The equation of the line in slope-intercept form is y = x.
Step-by-step explanation: We are given to find the equation in slope-intercept form of the line that is perpendicular to the line y - 4 = -(x - 6) and passes through the points (-2, -2).
PERPENDICULAR LINES: The product of the slopes of two perpendicular lines is -1.
The slope-intercept form of the given line is
\(y-4=-(x-6)\\\\\Rightarrow y-4=-x+6\\\\\Rightarrow y=-x+6+4\\\\\Rightarrow y=-x+10.\)
So, slope of the line, m = co-efficient of x = 1.
Let 'n' be the slope of the perpendicular line, so we have
\(m\times n=-1\\\\\Rightarrow -1\times n=-1\\\\\Rightarrow n=1.\)
Therefore, the slope-intercept form of the line with slope n = 1 and passing through the point (-2, -2) will be
\(y-(-2)=n\{x-(-2)\}\\\\\Rightarrow y+2=x+2\\\\\Rightarrow y=x.\)
Thus, the slope-intercept form of the line is y = x.
