Final answer:
Using the slope formula (y₂ - y₁) / (x₂ - x₁), the slope of the line through points (3,5) and (6,10) is calculated to be 5/3.
Step-by-step explanation:
To find the slope of the line through the points (3,5) and (6,10), we use the slope formula:
m = (y₂ - y₁) / (x₂ - x₁). Substituting the given points into the formula, we get m = (10 - 5) / (6 - 3) which simplifies to m = 5 / 3. Therefore, the slope of the line is 5/3.
This calculation involves the difference in y-coordinates (rise) and the difference in x-coordinates (run), reflecting the concept illustrated by FIGURE A1 Slope and the Algebra of Straight Lines where a consistent slope on a line graph shows a constant rise over run.