Final answer:
The displacement x at time t = 3 s for a linear graph with a slope of 3 m/s and a y-intercept of -15 m is -6 m. This is calculated using the slope-intercept form of the linear equation.
Step-by-step explanation:
The problem describes a linear relationship between displacement (x) and time (t), represented on a graph that intersects the vertical axis (displacement-axis) at -15 m and the horizontal axis (time-axis) at 5 s. This indicates the initial displacement is -15 m and it takes 5 seconds for the displacement to reach zero. The slope of this line, which is the change in displacement per unit time (rate of change), can be calculated using the intercepts given.
The slope (m) is the rise over run: m = (0 - (-15 m)) / (5 s - 0 s) = 15 m / 5 s = 3 m/s. This is the velocity of the object since velocity is the rate of change of displacement concerning time. To find the displacement at t = 3 s, we use the equation of a line, x = mt + b, where b is the y-intercept (-15 m in this case).
So, x at t = 3 s would be (3 m/s * 3 s) + (-15 m) = 9 m - 15 m = -6 m. Therefore, the value of x corresponding to t = 3 s is -6 m.