The given statement is False.

Reason: The slope of the line passing through the points (x1,y1) and (x2,y2) is given by

\(\displaystyle{m}=\frac{{{y}{1}-{y}{2}}}{{{x}{1}-{x}{2}}}\)

Using this formula the slope of the line through (−8,2) and (−1,4) is given by

\(\displaystyle{m}{1}=\frac{{{2}-{4}}}{{-{8}+{1}}}=\frac{{2}}{{7}}\)

And the slope of the line through (0,−4) and (−7,7) is

\(\displaystyle{m}{2}=\frac{{-{4}-{7}}}{{{0}+{7}}}=-{\left(\frac{{11}}{{7}}\right)}\)

Since, the slopes m1 and m2 are not equal or not proportional, the given lines are not parallel.

Reason: The slope of the line passing through the points (x1,y1) and (x2,y2) is given by

\(\displaystyle{m}=\frac{{{y}{1}-{y}{2}}}{{{x}{1}-{x}{2}}}\)

Using this formula the slope of the line through (−8,2) and (−1,4) is given by

\(\displaystyle{m}{1}=\frac{{{2}-{4}}}{{-{8}+{1}}}=\frac{{2}}{{7}}\)

And the slope of the line through (0,−4) and (−7,7) is

\(\displaystyle{m}{2}=\frac{{-{4}-{7}}}{{{0}+{7}}}=-{\left(\frac{{11}}{{7}}\right)}\)

Since, the slopes m1 and m2 are not equal or not proportional, the given lines are not parallel.