Final answer:
The equation of the line passing through the points (2,5) and (7,20) is y = 3x - 1, found by calculating the slope as 3 and using the point-slope form to find the y-intercept as -1.
Step-by-step explanation:
To find the equation of the line containing the points (2,5) and (7,20), we need to calculate the slope and the y-intercept. The slope (m) is the rise over the run. Using the two points:
m = (Y₂ - Y₁) / (X₂ - X₁) = (20 - 5) / (7 - 2) = 15 / 5 = 3
Now we have m = 3. To find the y-intercept (b), we use one of the given points and the slope in the equation y = mx + b.
5 = 3(2) + b
b = 5 - 6
b = -1
Therefore, the equation of the line is y = 3x - 1.
Complete question:
Find the equation of the line containing the points (2,5) and (7,20).