A linear function passes through the origin and the point (2,5). What is its equation?

A linear function passes through the origin and the point (2,5). What is its equation?

• A. y = (5/2)x
• B. y = (2/5)x
• C. y = x
• D. y = (5/2)x + 1

Answer: (A)

To describe a line in slope-intercept form, use y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through the origin, b = 0, so the equation is y = mx. Using the two known points (0,0) and (2,5), the slope is m = (5 − 0)/(2 − 0) = 5/2. So the equation is y = (5/2)x, which indeed passes through both the origin and (2,5). If the slope were 2/5, y would be 4/5 at x = 2, not 5. If the slope were 1, y would be 2 at x = 2. If there were a y-intercept of 1, the line wouldn’t pass through the origin.

To describe a line in slope-intercept form, use y = mx + b, where m is the slope and b is the y-intercept. Since the line passes through the origin, b = 0, so the equation is y = mx. Using the two known points (0,0) and (2,5), the slope is m = (5 − 0)/(2 − 0) = 5/2. So the equation is y = (5/2)x, which indeed passes through both the origin and (2,5). If the slope were 2/5, y would be 4/5 at x = 2, not 5. If the slope were 1, y would be 2 at x = 2. If there were a y-intercept of 1, the line wouldn’t pass through the origin.