Answer: The equation of the line passing through the points (1, -1, 2) and (0, 2, -3) is: y = 3x - 4.
Explanation:
To find the equation of a line passing through two points, we can use the point-slope form of a line. The point-slope form of a line is given by:
y - y1 = m(x - x1)
where m is the slope of the line, (x1, y1) is a point on the line, and (x, y) are the coordinates of any other point on the line.
Step 1: Find the slope of the line (m)
The slope of the line can be found using the two points:
m = (y2 - y1) / (x2 - x1)
Plug in the values of x1, x2, y1, and y2 from the two given points:
m = (2 - (-1)) / (0 - 1) = 3
Step 2: Write the equation using the point-slope form
Use the point-slope form and the slope from step 1, and one of the given points:
y - (-1) = 3(x - 1)
Step 3: Simplify the equation
y + 1 = 3x - 3
Step 4: Solve for y
y = 3x - 4
So, the equation of the line passing through the points (1, -1, 2) and (0, 2, -3) is y = 3x - 4.