Which is the equation in slope-intercept form of the line through (2,3) and (6,7)?

Which is the equation in slope-intercept form of the line through (2,3) and (6,7)?

• A. y = x + 3
• B. y = x - 1
• C. y = 2x + 1
• D. y = x + 1

Answer: (D)

To find the equation in slope-intercept form, start by determining the slope from the two points. The rise is 7 − 3 = 4 and the run is 6 − 2 = 4, so the slope is 4/4 = 1. With slope m = 1, the line has form y = mx + b, which simplifies to y = x + b. Use one of the points to solve for b; plug in (2, 3): 3 = 1·2 + b, so b = 1. Therefore the equation is y = x + 1. This matches the required line through both points, since plugging x = 2 gives y = 3, and plugging x = 6 gives y = 7. If you test other intercepts with slope 1, they won’t make both points satisfy the equation (for example, y = x + 3 would give y = 5 when x = 2, which misses the point 2,3).

To find the equation in slope-intercept form, start by determining the slope from the two points. The rise is 7 − 3 = 4 and the run is 6 − 2 = 4, so the slope is 4/4 = 1. With slope m = 1, the line has form y = mx + b, which simplifies to y = x + b. Use one of the points to solve for b; plug in (2, 3): 3 = 1·2 + b, so b = 1. Therefore the equation is y = x + 1.

This matches the required line through both points, since plugging x = 2 gives y = 3, and plugging x = 6 gives y = 7. If you test other intercepts with slope 1, they won’t make both points satisfy the equation (for example, y = x + 3 would give y = 5 when x = 2, which misses the point 2,3).