Final answer:
The equation of the line in simplest form passing through the points (4,-1) and (11,6) is y = x - 5, determined by calculating the slope and applying it to the point-slope form of the equation.
Step-by-step explanation:
The student is asking for the equation of a line in simplest form that passes through the points (4,-1) and (11,6). To find this equation, we need to determine the slope of the line and use the point-slope form.
The slope, m, can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.
Applying this formula to the given points, the slope is (6 - (-1)) / (11 - 4) = 7/7 = 1.
Now we can use one of the points and the slope to write the equation in point-slope form, which is y - y1 = m(x - x1).
Choosing the point (4, -1), the equation becomes y - (-1) = 1(x - 4), simplifying to y = x - 5.
This is the equation of the line in simplest form.