Final answer:
The slope of the line is determined by dividing the change in y (Ay) by the change in x (Ax). Given Ax = -16 and Ay = 4, the slope (m) is -1/4, meaning the line slopes downward from left to right at a constant rate along its length.
Step-by-step explanation:
To determine the slope of the line based on given changes in x (Ax) and changes in y (Ay), we can use the formula for slope (m) which is the ratio of the vertical change (rise) to the horizontal change (run). The question provides us with Ax = -16 and Ay = 4 which indicates that for a certain interval along the line, x decreases by 16 units while y increases by 4 units.
Slope (m) can be calculated using the slope formula:
m = ∆y / ∆x
Therefore, in our case, m = 4 / (-16) = -1/4.
The negative sign indicates that the line slopes downwards from left to right, and the value of 1/4 means that for every move to the left by 4 units along the x-axis, the line moves down by 1 unit on the y-axis. Note that regardless of the other terms in a line's equation, the slope remains constant along the entire length of a straight line. As shown in our reference equations, the line of best fit y = -173.5 + 4.83x and the variations Y2 and Y3 all share the same slope (4.83), and this value is analogous to our calculation result, representing how steeply the line is inclined.