Final answer:
The equation of a straight line is given by y = mx + b, with 'm' representing slope and 'b' the y-intercept. For Figure A1, the equation is y = 3x + 9, given the slope is 3 and the y-intercept is 9. Always confirm that units are consistent and answers are reasonable after calculating.
Step-by-step explanation:
Writing the equation of a straight line involves understanding the relationship between the slope (m) and the y-intercept (b). Using Figure A1 as an example, we can deduce that the slope of the line is the rate at which y increases for every unit increase in x, which is shown to be 3 for this particular line. Moreover, the y-intercept is the point where the line crosses the y-axis, which is given as 9 in our example.
The correct form of the equation for a straight line is y = mx + b, where 'm' is the slope and 'b' is the y-intercept. To write the equation of the line depicted in Figure A1 correctly, you would use the identified slope of 3 and y-intercept of 9 to form the equation y = 3x + 9. This is a critical step, as it ensures all values are in the right units before plugging them into the equation.
Remember, when you enter your data into a calculator or computer to derive a linear equation, be sure the units are consistent, and round off your results to four decimal places if necessary. After calculating your answer, always check to make sure the units are correct and that the numbers involved are reasonable, connecting back to our initial examination of whether the answer makes sense.