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. $$T(h)=48.5-2.5h$$ 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 $B$ : $$f(x)=15x+13$$ 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. $$\text{Unknown environment 'tabular'}$$ $$\text{Unknown environment 'tabular'}$$ 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.