What you’ll learn
Write equations of geometric lines.
Key idea
Find rise/run, then the ordinate where x equals zero for the intercept.
Slope and the point at x zero jointly fix the line; another ordinate is not automatically the intercept.
Worked example
Enter the exact value or ordered values in the format requested below.
A straight path goes through A=(0,3) and B=(1,-1). Write the full exact line equation in x and y.
- Slope=(-1-(3))/1=-4; the point at x=0 fixes intercept 3.
- The equation y=-4x+3 gives both supplied point ordinates.
Answer: y=-4x+3
Quick Check
Choose which candidate representation satisfies the requirements of 'Write equations of geometric lines' and justify the choice.
A straight path goes through A=(0,-4) and B=(1,-6). Candidate equations are y=-2x-4, y=-2x-6, y=2x-4. Select the equation satisfying both points with slope/intercept evidence.