Question

on the coordinate plane shown, points a, b, c, and d lie on the same line. select from the drop - down menus to correctly complete the sentence.
on the coordinate plane shown, points a, b, c, and d lie on the same line. select from the drop - down menus to correctly complete the sentence.
the slope of \\(\overline{ab}\\) is choose the slope of \\(\overline{cd}\\) because the ratio of
the vertical change to the horizontal change between points a and b is
choose the ratio of the vertical change to the horizontal change
between points c and d
the options for the first drop - down are: greater than, equal to, less than; the options for the second drop - down are: greater than, equal to, less than

Explanation:

Step1: Encontrar la pendiente de \(AB\)

Tomar \(A(-2,6)\) y \(B(0,1)\). La fórmula de la pendiente \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Entonces \(m_{AB}=\frac{1 - 6}{0-(-2)}=\frac{-5}{2}\)

Step2: Encontrar la pendiente de \(CD\)

Tomar \(C(1,-3)\) y \(D(3,-8)\). Usando la fórmula de la pendiente \(m=\frac{y_2 - y_1}{x_2 - x_1}\), \(m_{CD}=\frac{-8-(-3)}{3 - 1}=\frac{-5}{2}\)

Answer:

The slope of \(\overline{AB}\) is equal to the slope of \(\overline{CD}\) because the ratio of the vertical change to the horizontal change between points \(A\) and \(B\) is equal to the ratio of the vertical change to the horizontal change between points \(C\) and \(D\)