So something like this, then?
The data from your table is in rows 4-7 of columns A, B and C.
This is converted to the reciprocal values in rows 4-7 of columns E, F and G respectively, header labels are added in row 1 (a header row), and cells E4-G7 are selected and a scatte chart created. When trend lines and the trend line equations are added, it resembles the one in your initial post.
Numbers will not plot trend lines extending beyond the supplied data, so to extend the two lines to meet the x axis, it is necessary to determine the pont where they would cross the x axis by solving the two expressions for y=0. This is done using the constant values in the equations for each slope, shown at top left of the chart, in formulas in E2 and E3.
E2: =(0-16.726)/6.9768
E3: =(0-16.653)/2.4468
Zeroes are added manually in G2 and F3 to specify the Y value where each slope meets the x axis, then the chart is selected again, and the selection rectangle enclosing cells E4-G7 is slid up two rows, then extended down two rows to include cells E2 - G7.
Touch-ups: The chart was stretched horizontally, major ticks added to the x axis, and a vertical line inserted and placed at the 0 point on the x as\xis to serve as the y axis.
Regards,
Barry