Final answer:
A line parallel to 4x - 2y = 6 has a gradient of 2. The gradient can be found by rearranging the equation into slope-intercept form, demonstrating that parallel lines share the same slope.
Step-by-step explanation:
The gradient or slope of a line describes how steep the line is. This can be determined by looking at the coefficients of the x and y terms in the equation of a line. In the case of the equation 4x - 2y = 6, we can rewrite it in slope-intercept form (y = mx + b) to find the gradient. We get the equation as y = 2x - 3, which tells us that the slope/gradient is 2. Therefore, a line that is parallel to the given line will also have a gradient of 2.
Other examples such as Y2 = -173.5 + 4.83x - 2(16.4) and Y3 = -173.5 + 4.83x + 2(16.4) indicate that their slopes are 4.83, which matches the slope of the line of best fit they're related to (y = -173.5 + 4.83x). According to FIGURE A1 in the reference material provided, the slope of the line there is 3, which illustrates how all lines along a straight line have the same slope.