Final answer:
To find the equation of a line parallel to y = -3/2x - 1 and passes through the point (4,6), we need to determine the slope of the given line and the y-intercept of the parallel line. The equation of the line is y = -3/2x + 9.
Step-by-step explanation:
To find the equation of a line that is parallel to y = -3/2x - 1 and passes through the point (4,6), we need to determine the slope of the given line. In the equation y = mx + b, where m is the slope, the given line has a slope of -3/2.
Since our parallel line should have the same slope, the equation will be y = -3/2x + b, where b is the y-intercept that we need to find.
To find the y-intercept, we substitute the values of the given point (4,6) into the equation and solve for b. Plugging in these values, we get 6 = (-3/2)(4) + b. Solving for b gives us b = 9.
Therefore, the equation of the line parallel to y = -3/2x - 1 and passing through the point (4,6) is y = -3/2x + 9.