Question

multiple choice 10 points
are the lines perpendicular? y = x + 3 and x + y = 6
yes, their slopes are negative reciprocals
no, their slopes are not negative reciprocals
essay 10 points
write the equation of the line that is perpendicular to the line given and through

Explanation:

Step1: Find the slope of the first line

The equation \(y = x + 3\) is in slope - intercept form \(y=mx + b\), where \(m\) is the slope. So, \(m_1=1\).

Step2: Find the slope of the second line

Rewrite \(x + y=6\) in slope - intercept form \(y=-x + 6\). Here, \(m_2=-1\).

Step3: Check the relationship between slopes

Two lines are perpendicular if \(m_1\times m_2=-1\). Substitute \(m_1 = 1\) and \(m_2=-1\), we get \(1\times(-1)=-1\).

Answer:

yes, their slopes are negative reciprocals