Final answer:
The equation for the line passing through the points (35, -66) and (0, 3) is approximately 1.9714x + y = 3.
Step-by-step explanation:
The equation for the line passing through the points (35, -66) and (0, 3) can be found using the point-slope form of the equation. The point-slope form is given by y - y1 = m(x - x1), where (x1, y1) are the coordinates of one point on the line and m is the slope. First, let's find the slope of the line using the formula: m = (y2 - y1) / (x2 - x1).
Given points: (35, -66) and (0, 3)
Slope: m = (3 - (-66)) / (0 - 35) = 69 / (-35) = -1.9714 (rounded to 4 decimal places)
Now, we can choose one of the points, let's say (0, 3), and substitute the coordinates and the slope into the point-slope form:
y - 3 = -1.9714(x - 0)
Expanding the equation gives:
y - 3 = -1.9714x
Finally, rearranging the equation to the standard form Ax + By = C, we have:
(1.9714)x + y = 3
Therefore, the equation for the line passing through the points (35, -66) and (0, 3) is approximately:
1.9714x + y = 3