Final answer:
To find the point-slope equation of the line through the points (-2, 6) and (1, 1), calculate the slope using the formula m = (y2 - y1) / (x2 - x1), which in this case is -5/3. Then apply one of the points to the point-slope equation formula y - y1 = m(x - x1) to arrive at the final equation: y - 6 = -5/3(x + 2).
Step-by-step explanation:
To complete the point-slope equation of the line that passes through the points (-2, 6) and (1, 1), we first need to calculate the slope of the line. The slope (m) of a line through two points (x1, y1) and (x2, y2) is given by:
m = \((y2 - y1) / (x2 - x1)\)
For our points (-2, 6) and (1, 1), this becomes:
m = \((1 - 6) / (1 - (-2))\) = \((-5) / (3)\) = \((-5/3)\)
So, the slope of our line is -5/3.
Now, we can use one of our points and the slope to write the point-slope form of the equation, which is:
y - y1 = m(x - x1)
Using the point (-2, 6), the equation becomes:
y - 6 = -5/3(x + 2)
This is the complete point-slope equation of the line through the given points.