Question

Determine the standard form of the equation of the line that passes through (6, -9) and (-8, 6)

Answer 1

9514 1404 393

Answer:

  A.  15x +14y = -36

Step-by-step explanation:

Since we are given two points, we can start with the 2-point form of the equation for a line.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (6 -(-9))/(-8 -6)(x -6) +(-9)

  y = 15/-14(x -6) -9

Multiplying by -14, we have ...

  -14y = 15x -90 +126

Adding 14y-36 to both sides gives ...

  -36 = 15x +14y . . . . matches choice A

The standard-form equation is ...

  15x +14y = -36

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Additional comments

It can be easier to start with the form ...

  (Δy)x -(Δx)y = (Δy)x1 -(Δx)y1 . . . . . where Δx = x2-x1 and Δy = y2-y1

This gives ...

  (6+9)x -(-8-6)y = 15(6) +14(-9)

  15x +14y = -36 . . . simplified

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You can also start with the slope-intercept form or the point-slope form, if you're more familiar with those. The result will be the same. I find it handy to be familiar with a number of different forms of the equation for a line.