Final answer:
The x-intercept is where a line crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0). Without the graph, exact values cannot be determined; however, the concept is essential in finding the numerical values of these intercepts.
Step-by-step explanation:
To determine the x- and y-intercepts of a line on a standard (x, y) coordinate plane, you must understand where the line crosses the x-axis and y-axis. The x-intercept is the point where the line crosses the x-axis, this occurs when y is zero. The y-intercept is the point where the line crosses the y-axis, which occurs when x is zero. Let's analyze the options given:
- a) X-intercept: 3, Y-intercept: 1: This means the line would cross the x-axis at (3,0) and the y-axis at (0,1).
- b) X-intercept: -3, Y-intercept: -1: This means the line would cross the x-axis at (-3,0) and the y-axis at (0,-1).
- c) X-intercept: 1, Y-intercept: 3: This implies the line would cross the x-axis at (1,0) and the y-axis at (0,3).
- d) X-intercept: -1, Y-intercept: -3: This suggests the line would cross the x-axis at (-1,0) and the y-axis at (0,-3).
Without the graph itself, identifying the exact figures is not possible, but the concept of finding intercepts on a coordinate plane is that for the x-intercept, y is zero and for the y-intercept, x is zero. You must look at where the line crosses each axis to determine the corresponding intercepts.