On a graph, there is a linear equation: y = -x - 3. I want the bottom part of the line instead of being in the middle of the 0 and -5, I want it to be a little closer to the -5. The top part of the line is fine where it is being in the middle of the -5 and 0.

Answer 1

To adjust the linear equation $y=-x-3$ so that the lower part of the line is closer to -5 on the y-axis, you can modify the y-intercept. The current y-intercept is -3, which positions the line where it intersects the y-axis.

If you want to shift the lower part of the line down closer to -5 while keeping the upper part around the middle of -5 and 0, you can lower the entire line. However, since specifying "a little closer to -5" is subjective, let's try a couple of variations.

1. Adjusting the y-intercept

To shift the line downwards, you can replace the y-intercept value of -3 with a lower value, like -4 or -4.5. Here are two options:

• Option 1: Change the equation to $y=-x-4$

  • This shifts the line down, making the lower part even closer to -5.

• Option 2: Change the equation to $y=-x-4.5$

  • This further pushes the line down toward -5.

Guidelines for Further Adjustments:

• If you keep $y=-x-4$, the y-intercept will be at -4, which will pull the lower part of the line closer to -5 but still allow the upper part to be relatively spaced between -5 and 0.
• Adjusting further can bring it closer to -5, but remember, the slope remains the same. Each of these adjustments maintains the line's characteristics but adjusts its position vertically.

You can choose the best modification based on how much closer you want the lower part of the line to be to -5.