In the xy-plane, a line passes through the points (2, 3) and (4, 7). What is the x-intercept of the line?
- A−1
- B−1/2
- C0
- D1/2
- E1
Find the x-intercept from two points
Try it before you scroll. Two minutes on the clock, then commit to an answer.
Correct answer: D
First get the slope: m = (7 − 3) / (4 − 2) = 4/2 = 2.
Now build the equation with one point, say (2, 3): y − 3 = 2(x − 2), which simplifies to y = 2x − 1.
The x-intercept is where y = 0: 0 = 2x − 1, so x = 1/2.
Verification with the other point: at x = 4, y = 2(4) − 1 = 7 ✓.
The traps:
- (A), −1, is the y-intercept (the line crosses the y-axis at (0, −1)). Reading “x-intercept” as “the intercept in the equation” is the single most common error here.
- (B), −1/2, comes from solving 2x + 1 = 0, a sign slip when moving the constant across the equals sign.
- (C), 0, assumes the line passes through the origin; it does not, since the y-intercept is −1.
Definition to hold onto: the x-intercept is the x-value where the graph crosses the x-axis, meaning y = 0. The y-intercept is the b in y = mx + b. The two are interchangeable only when the line passes through the origin.