Question

which graph has a slope of $-2$?
\bigcirc a)\

$$\begin{tikzpicture}scale=0.5 \\draw-> (-5,0) -- (5,0) noderight {$x$}; \\draw-> (0,-5) -- (0,5) nodeabove {$y$}; \\foreach \\x in {-4,-3,-2,-1,1,2,3,4} \\draw (\\x cm,1pt) -- (\\x cm,-1pt) nodeanchor=north {\\x}; \\foreach \\y in {-4,-3,-2,-1,1,2,3,4} \\draw (1pt,\\y cm) -- (-1pt,\\y cm) nodeanchor=east {\\y}; \\drawthick, blue (-2,0) -- (0,4); \ ode at (-2,0) below right {$(-2, 0)$}; \ ode at (0,4) above right {$(0, 4)$}; \\end{tikzpicture}$$

\bigcirc b)\

$$\begin{tikzpicture}scale=0.5 \\draw-> (-5,0) -- (5,0) noderight {$x$}; \\draw-> (0,-5) -- (0,5) nodeabove {$y$}; \\foreach \\x in {-4,-3,-2,-1,1,2,3,4} \\draw (\\x cm,1pt) -- (\\x cm,-1pt) nodeanchor=north {\\x}; \\foreach \\y in {-4,-3,-2,-1,1,2,3,4} \\draw (1pt,\\y cm) -- (-1pt,\\y cm) nodeanchor=east {\\y}; \\drawthick, blue (-2,2) -- (2,0); \ ode at (-2,2) above right {$(-2, 2)$}; \ ode at (2,0) below right {$(2, 0)$}; \\end{tikzpicture}$$

\bigcirc c)\

$$\begin{tikzpicture}scale=0.5 \\draw-> (-5,0) -- (5,0) noderight {$x$}; \\draw-> (0,-5) -- (0,5) nodeabove {$y$}; \\foreach \\x in {-4,-3,-2,-1,1,2,3,4} \\draw (\\x cm,1pt) -- (\\x cm,-1pt) nodeanchor=north {\\x}; \\foreach \\y in {-4,-3,-2,-1,1,2,3,4} \\draw (1pt,\\y cm) -- (-1pt,\\y cm) nodeanchor=east {\\y}; \\drawthick, blue (1,4) -- (3,0); \ ode at (1,4) above right {$(1, 4)$}; \ ode at (3,0) below right {$(3, 0)$}; \\end{tikzpicture}$$

Explanation:

Step1: Recall slope formula

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Calculate slope for Option A

Points: \((-2, 0)\) and \((0, 4)\).
\( m=\frac{4 - 0}{0 - (-2)}=\frac{4}{2} = 2 \). Not \(-2\).

Step3: Calculate slope for Option B

Points: \((-2, 2)\) and \((2, 0)\).
\( m=\frac{0 - 2}{2 - (-2)}=\frac{-2}{4}=-\frac{1}{2} \). Not \(-2\).

Step4: Calculate slope for Option C

Points: \((1, 4)\) and \((3, 0)\).
\( m=\frac{0 - 4}{3 - 1}=\frac{-4}{2}=-2 \). This matches.

Answer:

C. The graph with points \((1, 4)\) and \((3, 0)\) (the third graph)