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- From: Mathematics, Algebra
- Posted on: Tue 19 Jan, 2016
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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.
1.True or false. The slope of a horizontal line is undefined.
2.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.
3.True or false. The y-intercept of the straight line with equation Ax + By + C = 0 is -C/B (B ? 0).
4.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 y=-1/m(x)+c , where c is a constant.
5.True or false. Suppose an asset is being depreciated linearly. Then the rate of depreciation of the asset is given by the negative of the slope of the depreciation line.
6.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.
7.True or false. The least-squares line must pass through at least one of the data points.
Solution Description

(1) False

Consider the points (2, 3) and (5, 3) which lie on a horizontal line. Slope of the line is (3 – 3)/(5 – 2) = 0. This proves that slope of a horizontal line is not undefined.

(2) True

Let P be (h, k). Equation of L is y – k = (-3/4)