find the slope of the line passing through the points (-7,2) and (9,6).

Explanation:

Step1: Identify the formula for slope

The formula for 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: Substitute the given points into the formula

Here, (x_1=-7,y_1 = 2,x_2=9,y_2=6). So (m=\frac{6 - 2}{9-(-7)}).

Step3: Simplify the numerator and denominator

The numerator (6 - 2=4), and the denominator (9-(-7)=9 + 7=16). Then (m=\frac{4}{16}).

Step4: Reduce the fraction

(\frac{4}{16}=\frac{1}{4}) (divide numerator and denominator by 4).

Answer:

(\frac{1}{4})