Question

london wants to find the slope of the line. she says she can use either points a and b or points b and c to find the slope.
is london correct? why or why not?
london is correct.
the triangles are similar,
so the ratios of corresponding side
lengths are equal.
what is the slope of the line?

Explanation:

Step1: Find the slope using points A and B

Let \(A=(1,2)\) and \(B=(2,4)\).
The slope formula is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
So, \(m_{AB}=\frac{4 - 2}{2 - 1}=\frac{2}{1} = 2\).

Step2: Find the slope using points B and C

Let \(B=(2,4)\) and \(C=(4,8)\).
Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\),
\(m_{BC}=\frac{8 - 4}{4 - 2}=\frac{4}{2}=2\).

Answer:

\(2\)