Final answer:
The slope of the function's graph is -1/2 and the y-intercept is 3. The equation for the function is y = -1/2x + 3.
Step-by-step explanation:
The slope of a linear function's graph represents the rate of change between the x-values and y-values. It can be calculated by taking the difference in y-values (rise) and dividing it by the difference in x-values (run). To find the slope, we can choose two points from the table of values and use the slope formula: m = (y2 - y1) / (x2 - x1). Using the points (0, 3) and (4, 1), we have m = (1 - 3) / (4 - 0) = -2/4 = -1/2.
The y-intercept of a linear function's graph is the point where the line crosses the y-axis. To find the y-intercept, we can choose any point from the table of values and substitute its x and y values into the equation y = mx + b, where m is the slope and b is the y-intercept. Using the point (0, 3), we have 3 = -1/2(0) + b, which simplifies to 3 = b. Therefore, the y-intercept is b = 3.
Combining the slope and y-intercept, we can write the equation for the linear function as y = -1/2x + 3.