# Solve and Prove the Following Statements

*label*Mathematics

*timer*Asked: Sep 3rd, 2014

**Question description**

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
*L*_{1}has equation*y*=*mx*+*b*, where*m*and*b*are constants with*m*≠0,then an equation of a line*L*_{2}perpendicular to*L*_{1}has the form , where*C*is a constant. - 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 (*x*_{0},*p*_{0}) is the breakeven point, then*P*(*x*) >*P*(*x*_{0}) if*x*>*x*_{0}, where*P*is the profit function.

7. True or false. The least-squares line must pass through at least one of the data points.