Final answer:
The slope of the linear equation y=1/8x +3 is 1/8, and the y-intercept is 3. The slope indicates a rise of 1/8 on the y-axis for every unit increase on the x-axis, while the y-intercept is the point where the line intersects with the y-axis at (0, 3).
Step-by-step explanation:
To find the slope and the y-intercept of the linear equation y=1/8x +3, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
In the equation y=1/8x +3, the coefficient of x, which is 1/8, represents the slope. Therefore, the slope (m) is 1/8. This means that for every increase of 1 on the horizontal axis (x), there is a rise of 1/8 on the vertical axis (y). The slope is consistent along the entire length of a straight line.
The constant term, which is 3 in this equation, represents the y-intercept (b). This is the point where the line crosses the y-axis, thus the y-intercept is 3. Consequently, the line crosses the y-axis at the point (0, 3).