A line has slope 2 and passes through the origin. What is the y-intercept?

A line has slope 2 and passes through the origin. What is the y-intercept?

• A. 0
• B. 2
• C. -2
• D. 1

Answer: (A)

The y-intercept is the value of b in the slope-intercept form y = mx + b, and it tells where the line crosses the y-axis (the point where x = 0). Because the line passes through the origin, its crossing with the y-axis is at (0, 0), so the y-intercept must be 0. You can see this by writing the equation with the given slope: y = 2x + b. Since the origin lies on the line, plug in x = 0 and y = 0: 0 = 2(0) + b, which gives b = 0. Therefore the y-intercept is 0. The other values would place the line crossing the y-axis at those numbers, but that would mean the line doesn’t pass through the origin.

The y-intercept is the value of b in the slope-intercept form y = mx + b, and it tells where the line crosses the y-axis (the point where x = 0). Because the line passes through the origin, its crossing with the y-axis is at (0, 0), so the y-intercept must be 0. You can see this by writing the equation with the given slope: y = 2x + b. Since the origin lies on the line, plug in x = 0 and y = 0: 0 = 2(0) + b, which gives b = 0. Therefore the y-intercept is 0. The other values would place the line crossing the y-axis at those numbers, but that would mean the line doesn’t pass through the origin.