Final answer:
To find the equation of a parallel line passing through the point (2, 1), use the same slope as the given line (2.0 km/min) and solve for the y-intercept using the point-slope form of the equation. The resulting equation for the line parallel to the given line and passing through point (2, 1) is y = 2.0x - 3.
Step-by-step explanation:
The student is asking to find the equation of a line that is parallel to a given line and that passes through a specific point. Since lines that are parallel have identical slopes, we can use the same slope as the given line for our new line. The original line's equation is given by y = (2.0 km/min) x, which implies a slope of 2.0 km/min. Furthermore, since the original equation does not have a y-intercept (b = 0), we only need to find the new y-intercept that allows the line to pass through the point (2, 1). Using the formula y = mx + b, where m is the slope and b is the y-intercept, we plug in the slope 2.0 km/min and the point (2, 1) to solve for b.
Step-by-step solution:
- Write the equation using the known slope and point form: y - y1 = m(x - x1).
- Plug in the slope and the point into the equation: y - 1 = 2.0(x - 2).
- Simplify and solve for y: y = 2.0x - 4 + 1.
- The final equation of the line is y = 2.0x - 3.