Final answer:
The slope of the line is 3, and the equation is y = 3x + 9. To find the values for a and b from the point (a, 8), there appears to be an error as the calculation yields a non-integer value for a. The y-coordinate when x = 0 is 9.
Step-by-step explanation:
To find the slope of the line, we can use the slope formula, which is the change in y divided by the change in x (rise over run). Given the slope information from Figure A1, we know that for every increase of 1 on the horizontal axis (x), there is a rise of 3 on the vertical axis (y). Therefore, the slope of the line is 3.
The equation of a straight line is usually given in the form y = mx + b, where m is the slope and b is the y-intercept. From the provided information, we know that the y-intercept is 9, and since we've determined the slope to be 3, the equation for the line is y = 3x + 9.
To find the values for a and b, we use the fact that all points given in the question must satisfy the equation of the line. If we plug in (a, 8) into the equation y = 3x + 9 and solve for a, we get:
a = (8 - 9) / 3 = -1/3, which does not correspond to a point with a whole number coordinate, suggesting there may be an error or typo in the initial question. However, since we are not provided with the value of b in the coordinates, and assuming (a, 8) was supposed to be on the line, it cannot be found. Lastly, the y-coordinate when x = 0 can be found by substituting x with 0 in the equation, yielding y = 3(0) + 9, which simplifies to y = 9.