Final answer:
To define a function with the points (1,1) and (8,2), use the slope-intercept form of a line.
Step-by-step explanation:
To define a function with the points (1,1) and (8,2), we need to find the equation of the line that passes through these two points. The equation of a line can be written in the form y = mx + b, where m is the slope and b is the y-intercept.
- First, find the slope (m) by using the formula: m = (y2 - y1) / (x2 - x1). In this case, the coordinates of the points are: (x1, y1) = (1,1) and (x2, y2) = (8,2).
- Substitute the values into the formula: m = (2 - 1) / (8 - 1) = 1/7.
- Next, find the y-intercept (b) by substituting the slope and one of the points into the equation.
- Using the point (1,1), we have: 1 = (1/7)(1) + b.
- Solve for b: b = 1 - 1/7 = 6/7.
Therefore, the equation of the line that passes through the points (1,1) and (8,2) is y = (1/7)x + 6/7.