91Ó°ÊÓ

Write an equation ( \(a\) ) in standard form and ( \(b\) ) in slope-intercept form for the line described. See Example \(6 .\) Find \(k\) so that the line through \((4,-1)\) and \((k, 2)\) is (a) parallel to \(3 y+2 x=6\) (b) perpendicular to \(2 y-5 x=1\)

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. $$\text { through }(3,-4), m=-\frac{1}{3}$$

Graph each function. $$y=(x-4)^{2}$$

Let \(f(x)=-3 x+4\) and \(g(x)=-x^{2}+4 x+1 .\) Find and simplify each of the following. $$f(x+2)$$

Let \(f(x)=-3 x+4\) and \(g(x)=-x^{2}+4 x+1 .\) Find and simplify each of the following. $$f(a+4)$$

Find the coordinates of the points of intersection of the line \(y=1\) and the circle centered at \((3,0)\) with radius 2.

Graph the line passing through the given point and having the indicated slope. Plot two points on the line. $$\text { through }(-2,-3), m=-\frac{3}{4}$$

Graph each function. $$y=(x-2)^{2}$$

Lumber that is used to frame walls of houses is frequently sold in multiples of 2 ft. If the length of a board is not exactly a multiple of \(2 \mathrm{ft}\), there is often no charge for the additional length. For example, if a board measures at least \(8 \mathrm{ft}\), but less than \(10 \mathrm{ft}\), then the consumer is charged for only \(8 \mathrm{ft}\). (a) Suppose that the cost of lumber is \(\$ 0.80\) every \(2 \mathrm{ft}\). Find a formula for a function \(f\) that computes the cost of a board \(x\) feet long for \(6 \leq x \leq 18\) (b) Determine the costs of boards with lengths of \(8.5 \mathrm{ft}\) and \(15.2 \mathrm{ft}\).

Let \(f(x)=-3 x+4\) and \(g(x)=-x^{2}+4 x+1 .\) Find and simplify each of the following. $$f(2 m-3)$$