if you think the statement is true, then prove it. On the
other hand, if you think the statement is false, then give an example that
disproves the statement. For example, the statement "If a and b are
real numbers, then a - b = b - a"
is false and an example that disproves it may be constructed by taking a =
3 and b = 5. For these values of a and b,
we find a - b = 3 - 5 = -2 but b - a =
5 - 3 = 2 and this shows that a - b ≠ b - a.
Such an example is called a ≠counterexample.
- True or false. The slope
of a horizontal line is undefined.
- True or false. Suppose the
slope of a straight line L is -3/4 and P is
a given point on L. If Q is a point on L lying
2 units to the right of P, then Q is situated
3/2 units below P.
- True or false. The y-intercept
of the straight line with equation Ax + By + C =
0 is -C/B (B ≠ 0).
- True or false. If a
line L1 has equation y = mx
+ b, where m and b are
constants with m ≠0,then an equation of a
line L2 perpendicular to L1 has
the form , where C is
- True or false. Suppose an
asset is being depreciated linearly. Then the negative of the slope of the
depreciation line gives the rate of depreciation of the asset.
- True or false. If R and C are
linear revenue and cost functions, respectively, and (x0, p0)
is the breakeven point, then P (x) > P (x0)
if x > x0, where P is
the profit function.
True or false. The least-squares line must pass
through at least one of the data points.