Final answer:
To find the slope 'm' for a line described by the equation y = mx - 2 that passes through given points, plug the coordinates of each point into the equation and solve for 'm'. This provides the specific slope for the line at each of those points.
Step-by-step explanation:
For the equation y = mx - 2, the value of m represents the slope of the line, which is the change in y divided by the change in x as the line moves from one point to another. To find the slope m when the line passes through a certain point, we can use the coordinates of the point to substitute into the equation and solve for m.
- For point a (2, 3): Plug x = 2 and y = 3 into the equation to get 3 = 2m - 2. Solving for m gives m = 2.5.
- For point b (3, 1): Plug x = 3 and y = 1 into the equation to get 1 = 3m - 2. Solving for m gives m = 1.
- For point c (4, 0): Plug x = 4 and y = 0 into the equation to get 0 = 4m - 2. Solving for m gives m = 0.5.
- For point d (5, -1): Plug x = 5 and y = -1 into the equation to get -1 = 5m - 2. Solving for m gives m = 0.2.
To determine these values, you take the given y value, substitute it along with the x value into the given linear equation, and solve for m. Doing this for each point individually, you obtain a specific slope for the line that passes through each of those points.