Match the information about each graph with the correct linear equation. \[ \begin{array}{ll}\text { Information } & \text { Linear Equations } \\ \begin{array}{ll}\text { (a) The graph of the equation has } y \text {-intercept }(0,-4) & \text { A. } y=3 x \\ \text { (b) The graph of the equation has }(0,0) \text { as } x \text {-intercept and } y \text {-intercept. } & \text { B. } y=3 \\ \text { (c) The graph of the equation does not have an } x \text {-intercept. } & \text { C. } 2 x+y=-4 \\ \text { (d) The graph of the equation has } x \text {-intercept }(5,0) & \text { D. } x-5=0\end{array}\end{array} \]

Solve the equation by factoring. Select the correct solution. \( 6 x^{2}-5 x-4=0 \) \( \begin{array}{ll}\text { O } & \text { A) } x=-\frac{4}{3},-\frac{1}{2} \\ \text { O } & \text { B) } x=-\frac{1}{2}, \frac{4}{3} \\ \text { O } & \text { C) } x=-\frac{4}{3}, \frac{1}{2} \\ \text { - } & \text { D) } x=\frac{1}{2}, \frac{4}{3}\end{array} \)

Solve the equation. \( \ln (8 \mathrm{x}+15)-\ln \mathrm{x}=\ln 9 \) Select the correct choice below and, if necessary, fill in th A. The solution set is \( \{ \) B. The solution is the empty set. (Simplify your answer. Use a comma to separate a

Use the properties of logarithms to rewrite the expression. Simplify the res \( \log _{3} \frac{\sqrt{x} \sqrt[3]{y}}{w} \sqrt{z} \) Choose the correct answer. A. \( -\frac{1}{2} \log _{3} x-\frac{1}{3} \log _{3} y+5 \log _{3} w+\frac{1}{2} \log _{3} z \) B. \( \frac{1}{2} \log _{3} x+\frac{1}{3} \log _{3} y-5 \log _{3} w-\frac{1}{2} \log _{3} z \) C. \( { }^{2} \log _{3} x+3 \log _{3} y-5 \log _{3} w-2 \log _{3} z \) D. This cannot be simplified.

b. \( -0.5 p+\frac{1}{2} p-2.75+\frac{2}{3} \)

Consider the line \( y=\frac{5}{2} x-3 \). Find the equation of the line that is perpendicular to this line and passes through the point \( (2,-5) \). Find the equation of the line that is parallel to this line and passes through the point (2, -5). Note that the ALEKS graphing calculator may be helpful in checking your answer. Equation of perpendicular line: