Question: (10 points)

a) Determine the equation of the straight line through the point (-1, 5) with slope m = -1.

b) What is the slope of any line perpendicular to that in part (a)? Explain.

Solution: (a) The equation is

\[y-5=-\left( x-\left( -1 \right) \right)\,\,\,\Rightarrow \,\,\,y=-\left( x+1 \right)+5=-x-1+5\] \[\Rightarrow \,\,\,y=-x+4\]

(b) The slope will be \({{m}_{P}}=-\frac{1}{-1}=1\).

8. (15 points)

a) Sketch the graph of the equation 2y + 3x = 1. Show all work.

b) What is the slope of the line in part (a)? Use your graph and the slope of this line to briefly explain the meaning of slope.