*Remember, you can also enter this table of numbers in your Desmos calculator to find the slope and y-intercept.

Question

After you enter the table of numbers, in the next entry, enter yl~ mxl+b.
slope 2, y-intercept (0, 6.5)
slope -2, y-intercept (4,0)
slope -2.5, y-intercept (4,0)
slope 2.5, y-intercept (0,4)

Answer 1

It seems you are dealing with a set of linear equations based on the slopes and y-intercepts given. Let’s express the linear equations for each slope and y-intercept you mentioned.

1. Slope: 2, Y-intercept: (0, 6.5)
   The equation of the line can be written as: \[ y = 2x + 6.5 \]

2. Slope: -2, Y-intercept: (4, 0)
   To find the equation, we can use the point-slope form. The line passes through (4, 0): \[ y - 0 = -2(x - 4) \] Simplifying this gives: \[ y = -2x + 8 \]

3. Slope: -2.5, Y-intercept: (4, 0)
   Similar to the previous one: \[ y - 0 = -2.5(x - 4) \] Simplifying this gives: \[ y = -2.5x + 10 \]

4. Slope: 2.5, Y-intercept: (0, 4)
   The equation can be expressed simply as: \[ y = 2.5x + 4 \]

Summary of the Equations:

1. \( y = 2x + 6.5 \)
2. \( y = -2x + 8 \)
3. \( y = -2.5x + 10 \)
4. \( y = 2.5x + 4 \)

You can graph these equations in your Desmos calculator for visualization, and use the command yl~ mxl+b to test them with your calculated slope (m) and y-intercept (b). If you have any specific questions about this data or further assistance, feel free to ask!