Final answer:
The equation of the line with a slope of 8 and a y-intercept of 2 is y = 8x + 2. This equation is in slope-intercept form, directly translating into the line's angle and position on a coordinate plane.
Step-by-step explanation:
The student is asking for an equation of a line in slope-intercept form, which is expressed as y = mx + b. In this formula, m stands for the slope, and b represents the y-intercept. These parameters determine the shape and position of the line on a coordinate plane.
Given that the slope (m) is 8 and the y-intercept (b) is 2, the equation of the line is y = 8x + 2.
This is the canonical form of the equation for a line, showing a direct relationship between the values in the equation and the graphical representation. The slope indicates that for every increase of one unit in x, y increases by 8 units. The y-intercept indicates that the line crosses the y-axis at the coordinate point (0, 2).