Final answer:
The slope of a line represents the rate of change in y compared to x. It is constant for a straight line and can be calculated using two points on the line, or by knowing the increase in y for each unit increase in x. The slope of the provided line is 3.
Step-by-step explanation:
The student is asking how to find the slope of a straight line on a graph. To determine the slope, one must understand that it represents the rate at which the y-value changes with respect to the x-value. In this case, a line graph with an x-axis (horizontal axis) and a y-axis (vertical axis) is provided, where the line has a given y-intercept of 9 and a slope of 3. This means that for every unit increase in x, the value of y increases by 3 units.
To find the slope, a common strategy involves selecting any two points on the line. A graphical figure might show two points, for instance, (6.4 s, 2000 m) and (0.50 s, 525 m). Using these points, the slope is calculated using the formula: slope = (change in y) / (change in x), which gives:
slope = (2000 m - 525 m) / (6.4 s - 0.50 s) = (1475 m) / (5.9 s) = 250 m/s
This calculation shows that the slope is constant regardless of which two points are chosen, provided they lie on the straight line. Furthermore, the algebra of straight lines often involves the use of the equation y = mx + b, where m represents the slope and b represents the y-intercept. In this example, the line equation would be y = 3x + 9.