Thank you for the question and for including the print sample.
According to my understanding of the sixth bullet under section 184.108.40.206 of the Tactile Graphic Guidelines, you can present your line plot vertically so that its mixed number labels will fit. Doing that might look something like the attached image for a transcription using Nemeth Code within a UEB context.
(In that image, the first braille page contains the title of the line plot and then a TN that says "Full braille cells are used to represent print x's." On the next line of the TN is the word "Key". That is followed by a blank line and then, in 1-3, ⠸⠩⠀⠿⠀⠨⠅⠀⠼⠂⠀⠎⠞⠥⠙⠑⠝⠞⠀⠸⠱ followed unspaced by UEB's closing TN indicator. The second braille page begins with an opening Nemeth Code indicator followed by a blank line and then the uncontracted label Inches. Below that, the lines of the number line that is the foundation of the line plot are spurred/drawn in; the number labels that are printed below the number line are brailled to its left without numeric indicators; and the full cells that represent the x's used in print are brailled on the right side of the drawn-in number line shape. The number labels begin with 5 3/4 and proceed downward down the page. The number line is followed by a blank line and then the Nemeth Code terminator in cell 1.)