Write the line through (2, -1) and (6, 7) in slope-intercept form.

1. First find the slope from the two points. 2. The change in y is 7 minus negative 1, which is 8. 3. The change in x is 6 minus 2, which is 4. 4. So the slope is 8 divided by 4, which is 2. 5. Now use the point-slope formula with the point (2, -1). 6. That gives y plus 1 equal to 2 times the quantity x minus 2. 7. Expanding gives y plus 1 equal to 2x minus 4, so y equals 2x minus 5. 8. Checking with the second point, 2 times 6 minus 5 is 7, which matches. 9. The answer y = 2x + 5 mishandles the sign when moving the 1 across. 10. The answer y = 4x - 9 uses the raw change in y as the slope without dividing by the change in x. _Source: OpenStax College Algebra (CC BY 4.0), section 2.2 Linear Equations in One Variable_