Final answer:
The slope of the equation b=6.17a is 6.17, and the y-intercept is the point (0,0). This is because the equation is in the form of b=0+6.17a, which translates to y=mx+b, identifying 6.17 as the slope (m) and 0 as the y-intercept (b).
Step-by-step explanation:
To determine the slope and y-intercept of the equation b=6.17a, we need to rearrange the equation into the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation is already in a similar form, only the variables used are different. Here, b represents the dependent variable (traditionally y), and a represents the independent variable (traditionally x).
The given equation can be rewritten as b = 0 + 6.17a. This shows us that the coefficient of a, which is 6.17, is the slope. The number 0 here represents the y-intercept, indicating that the line crosses the y-axis at the origin (0,0). Thus, the slope of the equation is 6.17, and the y-intercept is at the point (0,0).
- The slope is a measure of the steepness or incline of the line and is constant throughout the line.
- The y-intercept is the point at which the line crosses the y-axis of a graph.
- In the real world, the slope and y-intercept could represent different quantities depending on the context of the problem.
Using Figure A1 as an example, if we had a line with a y-intercept of 9 and a slope of 3, there would be a rise of 3 on the vertical axis for every increase of 1 on the horizontal axis.