A line passes through (5,6) and (2,8). A second line passes through (7,1). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
bp
Jan 8, 2017

One specific point would be (4,3)

Explanation:

Slope of the line passing through (5,6) and (2,8) would be 8−62−5=−23

Slope of the line parallel to this one would also be −23. If the line passing through (7,1) also passes through a point (x,y), then its slope can also be expressed as y−1x−7

Then −23=y−1x−7. Solve this eq. for y.

y=17−2x3. Now assign any value to x and calculate the corresponding y. Thus there would be infinite number of points
satisfying the equation.

A specific point can be obtained by assigning the value x=4 for which y would be 3. this point would thus be (4,3).

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