Linear Equations and Inequalities

Scientists have found a relationship between the temperature and the height above a distant planet's surface. $T(h)$, given below, is the temperature in Celsius at a height of $h$ kilometers above the planet's surface. The relationship is as follows. \[ T(h)=48.5-2.5 h \] Complete the following statements. Let $T^{-1}$ be the inverse function of $T$. Take $x$ to be an output of the function $T$. That is, $x=T(h)$ and $h=T^{-1}(x)$. (a) Which statement best describes $T^{-1}(x)$ ? The ratio of the temperature (in degrees Celsius) to the number of kilometers, $x$. The height above the surface (in kilometers) when the temperature is $x$ degrees Celsius. The reciprocal of the temperature (in degrees Celsius) at a height of $x$ kilometers. The temperature (in degrees Celsius) at a height of $x$ kilometers. (b) $T^{-1}(x)=$ (c) $T^{-1}(33)=$

The graph of a function $h$ is shown below. Use the graph of the function to find its average rate of change from $x=-3$ to $x=3$. Simplify your answer as much as possible.

Rewrite the following equation in slope-intercept form: \(3x - 2y = 6\)

Solve the following linear equation: \( 3x - 7 = 2x + 5 \)

If a line passes through the points (4,7) and (2,3), find the equation of the line using the slope-intercept formula.

Given two points, (3, 7) and (5,11), find the linear equation that passes through these two points.

Find the equation of the line perpendicular to the line \(3x - 2y = 6\) and passing through the point \((2,-1)\).

Question 32 \( 1 \mathrm{pts} \) What is the average rate of change over the interval [1, 10]? Equation \( A \) Equation \( B \) : \[ f(x)=15 x+13 \] A: 15; B: 0 A: 5; B: 15 \( A: 15 ; B: 5 \) A: O; B: 15

Find the equation of the line parallel to the line \(3x - 4y = 8\) and passing through the point \((4,2)\).

Find the equation of the line parallel to the line \(y = 3x + 2\) and passing through the point \((4, -2)\)

Find the equation of the line perpendicular to the line \(3x - 2y = 6\) and passes through the point (1, 2).

Find the ordered pair solution for the following linear equation: \(2x+3y=6\)

4. Each table represents a proportional relationship. For each, find the constant of proportionality, and write an equation that represents the relationship. \begin{tabular}{|c|c|} \hline$s$ & $P$ \\ \hline 2 & 8 \\ \hline 3 & 12 \\ \hline 5 & 20 \\ \hline 10 & 40 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline$d$ & $c$ \\ \hline 2 & 6.28 \\ \hline 3 & 9.42 \\ \hline 5 & 15.7 \\ \hline 10 & 31.4 \\ \hline \end{tabular} Constant of proportionality: Constant of proportionality: Equation: $P=$ Equation: $C=$

Find the equation of the line that passes through the points (4, -3) and (2, -1) using the point-slope form.