Given C(x, 16), D(2,-4), E(-6, 14), andF(-2, 4), find the value of x so that CD || EF.

Answer:x=-6Step-by-step explanation:we know thatIf two lines are parallel, then their slopes are the sameIn this problemslope CD=slope EFThe formula to calculate the slope between two points is equal to[tex]m=\frac{y2-y1}{x2-x1}[/tex]step 1Find the slope EFwe haveE(-6,14) and F(-2,4)substitute the values in the formula[tex]m_E_F=\frac{4-14}{-2+6}\\m_E_F=\frac{-10}{4}\\m_E_F=-2.5[/tex]step 2Find the slope CDwe haveC(x, 16) and D(2, -4)substitute the values in the formula[tex]m_C_D=\frac{-4-16}{2-x}\\m_C_D=\frac{-20}{2-x}[/tex]Remember that[tex]m_C_D=m_E_F[/tex]so[tex]\frac{-20}{2-x}=-2.5[/tex][tex]-20=-5+2.5x\\2.5x=-20+5\\2.5x=-15\\x=-6[/tex]