A line passes through the points (3, 8) and (-6, 2). Write the equation of the line in slope-intercept form.

Slope-intercept form is y= mx + b

Slope m = (y2 - y1) / (x2 - x1)

m = (2 - 8) / (-6 - 3)

m = (-6)/(-9)

m = 2/3

Now we can solve using the point-slope form y - y1 = m(x - x1) using either point for our x1, y1 (doesn't matter which).

 

y - 8 = (2/3)(x - 3)       Here i used point (3, 8) and our slope (2/3) from above.

y - 8 = (2/3)x - 2          Distribute the (2/3)

y = (2/3)x + 6               Add 8 to both sides

 

Therefore the slope-intercept form is y = (2/3)x + 6

When solving for slope, (8 - 2)/( 3 - -6) is just as valid as (2 - 8)/(-6 - 3) but (8 - 2)/(-6- 3) is not. Keep the x's and y's in the same order as each other and the y's on top (rise over run).