Graph the line that passes through the points (3, -2)(3,−2) and (9, 2)(9,2) and determine the equation of the line.

  2x -3y = 12

Step-by-step explanation:

For some horizontal change Δx and some vertical change Δy between the two points, an equation of the line through points (x1, y1) and (x2, y2) can be written as ...

  Δy·x -Δx·y = Δy·(x1) -Δx·(y1)

Here, we have ...

  Δy = y2 -y1 = 2 -(-2) = 4

  Δx = x2 -x1 = 9 -3 = 6

So, our equation can be ...

  4x -6y = 4·3 -6·(-2) = 24

Factoring out a common factor of 2 makes the equation be ...

  2x -3y = 12 . . . . . . equation of the line in standard form

Solving for y gives the equation in slope-intercept form:

  y = 2/3x -4

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More conventional solution

Plotting the points and drawing the line, you see that the y-intercept is -4. You also see that there is a "rise" of 2 grid squares for each "run" of 3 grid squares. Thus the slope of the line is 2/3. With this information, you can write the equation directly in slope-intercept form:

  y = mx + b . . . . . . line with slope m and y-intercept b

  y = 2/3x -4 . . . . . . the line through the given points

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