Final answer:
To find the linear equation for the line that passes through the points (1,-6) and (4,0), calculate the slope, which is 2, and then use the point-slope form to write the equation as y = 2x - 8.
Step-by-step explanation:
To write a function based on the given points (1,-6) and (4,0), we first need to determine the slope (slope) of the line that connects them. The formula for the slope is (y2-y1)/(x2-x1), so plugging in our values, we get (0 - (-6)) / (4 - 1) which simplifies to 6/3 or 2. Therefore, our slope is 2.
Next, we use the point-slope form of a line, y - y1 = slope(x - x1), to create our function. Using the point (1, -6) and our slope of 2, our function becomes y - (-6) = 2(x - 1). Simplifying this, we get y + 6 = 2x - 2, and then y = 2x - 8. This is the linear equation for the line that passes through the points (1, -6) and (4, 0).