options: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
problem_activity: Samantha found the slope of the line that passed through the points
$${(2, 6)}$$
and
$${(-4, 8)}$$
. Her work is shown below.
$${{8-6\over {2-(-4)}} = {2\over 2+4 }= {2\over 6} = {1\over3}}$$
Samantha made an error in her work. Describe the error and then find the correct slope of the line through the two given points.


correct_option_index: 0