-4) B. (4, 0)
2 Points What is the x-intercept of the function graphed below? A. (0, -4) B. (4, 0)
The Correct Answer and Explanation is:
Correct Answer: (4, 0)
Explanation:
The question asks for the x-intercept of the graphed linear function. The x-intercept is the specific point on a graph where the line crosses the horizontal axis, which is known as the x-axis. A key property of any x-intercept is that its y-coordinate is always zero, as it lies directly on the x-axis. The general form of an x-intercept is (x, 0).
To find the x-intercept from the provided graph, we need to locate the point where the diagonal line intersects the horizontal x-axis. By visually tracing the line, we can see it crosses the x-axis to the right of the origin (the point where the x and y axes meet).
Next, we must determine the exact coordinates of this intersection point by reading the scale on the x-axis. The tick marks on the axis are labeled in increments of two: 2, 4, 6, and so on. The line clearly passes through the x-axis at the mark labeled “4”. Since this point is on the x-axis, its y-coordinate must be 0. Therefore, the coordinates of the x-intercept are (4, 0).
Let’s analyze the given options to confirm our answer.
- Option A, (0, -4): This point has an x-coordinate of 0, which means it lies on the vertical y-axis. Looking at the graph, the line crosses the y-axis at -4. This point, (0, -4), is the y-intercept, not the x-intercept.
- Option B, (-4, 0): This point represents an intersection with the x-axis at x = -4. However, the graph shows the line crossing the x-axis on the positive side, not the negative side.
Based on a direct analysis of the graph, the only correct x-intercept is the point (4, 0).
