Question

Finding the Equation of a Line

You have discovered another alien.

What is the equation of the line that provides the correct path to rescue this alien?

Answer 1

I don’t have the picture or coordinates, so I can’t write the specific line yet. Tell me either (a) two points on the path, (b) one point and the slope, or (c) the graph/screenshot, and I’ll give the exact equation.

Meanwhile, here are quick steps you can use depending on what you have:

1. Two points (x1,y1) and (x2,y2)
- Slope m = (y2 − y1)/(x2 − x1).
- Use point–slope form: y − y1 = m(x − x1).
- Solve for y to get slope–intercept form y = mx + b, if desired.

Example: points (1,2) and (4,8)
- m = (8−2)/(4−1) = 6/3 = 2
- y − 2 = 2(x − 1) → y − 2 = 2x − 2 → y = 2x

2. One point (x1,y1) and slope m
- Use point–slope: y − y1 = m(x − x1). Rearrange as needed.

Example: point (3,5), m = −1
- y − 5 = −1(x − 3) → y = −x + 8

3. Graph information (intercepts or rise/run)
- If you can read slope from rise/run and the y-intercept b from the graph, equation is y = mx + b.
- If the line is vertical (x = constant) there is no y = mx + b form; equation is x = a.

If you post the two points or upload the image, I’ll compute the exact rescue path equation for you.