Question

select the graph that correctly represents the following:
the line through $(-3,4)$ and $(2,-3)$.

Explanation:

Step1: Calculate the slope

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \((x_1,y_1)=(-3,4)\) and \((x_2,y_2)=(2,-3)\). Then \(m=\frac{-3 - 4}{2-(-3)}=\frac{-7}{5}=-\frac{7}{5}\). A positive - slope line rises from left - to - right, and a negative - slope line falls from left - to - right.

Step2: Analyze the first graph

The first graph has a positive slope (rises from left - to - right). Since we calculated a negative slope (\(m =-\frac{7}{5}\)), this graph is incorrect.

Step3: Analyze the second graph

The second graph has a negative slope (falls from left - to - right).

Step4: Analyze the third graph

The third graph has a positive slope (rises from left - to - right). Since we calculated a negative slope (\(m =-\frac{7}{5}\)), this graph is incorrect.

Answer:

The second graph.