Final answer:
To find the equation of the line that passes through the points (1,1) and (8,9), use the slope-intercept form of a linear equation, y = mx + b. The equation is y = 8/7x - 1/7.
Step-by-step explanation:
To find the equation of the line that passes through the points (1,1) and (8,9), we can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. First, find the slope using the formula: m = (y2 - y1) / (x2 - x1). Plug in the values from the given points: m = (9 - 1) / (8 - 1) = 8 / 7. Now that we have the slope, we can substitute one of the points and the slope into the equation and solve for b: 1 = (8/7)(1) + b. Simplifying, we get b = 1 - 8/7 = -1/7.
So, the equation of the line that passes through the points (1,1) and (8,9) is y = 8/7x - 1/7.