Final answer:
The linear function that passes through the points (8,8) and (-10, -11) is determined by first calculating the slope and then using one of the points to solve for the y-intercept. The resulting linear function is y = (19/18)x - 4/9.
Step-by-step explanation:
We are tasked to find the linear function given two points it passes through, which are (8,8) and (-10, -11). To do this, we can use the formula for the slope of a line (m), which is m = (y2 - y1) / (x2 - x1).
Applying the points to the formula, we get m = (-11 - 8) / (-10 - 8) = -19 / -18 = 19/18. We can now use one of the points and the slope to find the y-intercept (b) of the linear equation y = mx + b.
Using the point (8,8), we plug into the equation: 8 = (19/18)*8 + b. Simplifying, we find b = 8 - (19/18)*8. To avoid the decimals, multiply both sides by 18 to get 144 = 19*8 + 18b, which simplifies to 144 = 152 + 18b and further to -8 = 18b. Dividing by 18 gives us b = -8 / 18 or b = -4/9. Therefore, the equation of our linear function is y = (19/18)x - 4/9.