91Ó°ÊÓ

Draw the graph of each equation. Name any intercepts. $$\frac{2}{3} x-y=1$$

In Exercises 5 to \(10,\) the real Numbers \(a, b, c,\) and \(d\) are positive. Consider the quadrilateral with vertices at \(A(0,0)\) \(B(a, 0), C(b, c),\) and \(D(d, c)\) Explain why \(A B C D\) is a trapezoid. (GRAPH CANT COPY)

In Exercises 5 to \(10,\) the real Numbers \(a, b, c,\) and \(d\) are positive. Consider the quadrilateral with vertices at \(M(0,0)\) \(N(a, 0), P(a, b),\) and \(Q(0, b) .\) Explain why \(M N P Q\) is a rectangle. (GRAPH CANT COPY)

Find the midpoint of the line segment that joins each pair a) \((0,-3)\) and \((4,0)\) b) \((-2,5)\) and \((4,-3)\) c) \((3,2)\) and \((5,-2)\) d) \((a, 0)\) and \((0, b)\)

Find the slopes of the lines containing: a) \((2,-3)\) and \((4,5)\) b) \((3,-2)\) and \((3,7)\) c) \((1,-1)\) and \((2,-2)\) d) \((-2.7,5)\) and \((-1.3,5)\) c) \((a, b)\) and \((c, d)\) f) \((a, 0)\) and \((0, b)\)

Complete an analytic proof for each theorem. The line segments that join the midpoints of the consecutive sides of a rectangle form a rhombus.

Find the equation of the line described. Leave the solution in the form \(A x+B y=C\). The line has slope \(m=-\frac{2}{3}\) and contains \((0,5)\).

Find the equation of the line described. Leave the solution in the form \(A x+B y=C\). The line has slope \(m=-3\) and contains \((0,-2)\).

Find the midpoint of the line segment that joins each pair of points: a) \((-3,-7)\) and \((2,5)\) b) \((0,0)\) and \((-2,6)\) c) \((-a,-b)\) and \((a, b)\) d) \((2 a, 2 b)\) and \((2 c, 2 d)\)

Find the slopes of the lines containing: a) \((3,-5)\) and \((-1,2)\) b) \((-2,-3)\) and \((-5,-7)\) c) \((2 \sqrt{2},-3 \sqrt{6})\) and \((3 \sqrt{2}, 5 \sqrt{6})\) d) \((\sqrt{2}, \sqrt{7})\) and \((\sqrt{2}, \sqrt{3})\) e) \((a, 0)\) and \((a+b, c)\) f) \((a, b)\) and \((-b,-a)\)