6.2 Linear equations in one variable  (Page 8/15)

$\frac{x+2}{4}-\frac{x-1}{3}=2$

$\frac{3}{x}-\frac{1}{3}=\frac{1}{6}$

$2-\frac{3}{x+4}=\frac{x+2}{x+4}$

$\frac{3}{x-2}=\frac{1}{x-1}+\frac{7}{(x-1)(x-2)}$

$\frac{3x}{x-1}+2=\frac{3}{x-1}$

$\frac{5}{x+1}+\frac{1}{x-3}=\frac{-6}{x^2-2x-3}$

$\frac{1}{x}=\frac{1}{5}+\frac{3}{2x}$

$\left(0,3\right)$ with a slope of $\frac{2}{3}$

$\left(1,2\right)$ with a slope of $\frac{-4}{5}$

x -intercept is 1, and $\left(\mathrm{-2},6\right)$

y -intercept is 2, and $\left(4,\mathrm{-1}\right)$

$(\mathrm{-3},10)$ and $(5,\mathrm{-6})$

$\left(1,3\right)\text{ and }\left(5,5\right)$

parallel to $y=2x+5$ and passes through the point $\left(4,3\right)$

perpendicular to $\text{3}y=x-4$ and passes through the point $\left(\mathrm{-2},1\right)$ .

$\left(-2,0\right)$ and $\left(\mathrm{-2},5\right)$

$\left(1,7\right)$ and $\left(3,7\right)$

The slope is undefined and it passes through the point $\left(2,3\right).$

The slope equals zero and it passes through the point $\left(1,\mathrm{-4}\right).$

The slope is $\frac{3}{4}$ and it passes through the point $\text{(1,4)}\text{.}$

$\left(\mathrm{-1},3\right)$ and $\left(4,\mathrm{-5}\right)$

$\begin{array}{l}\\ \begin{array}{l}y=2x+7\hfill \\ y=\frac{-1}{2}x-4\hfill \end{array}\end{array}$

$\begin{array}{l}3x-2y=5\hfill \\ 6y-9x=6\hfill \end{array}$

$\begin{array}{l}y=\frac{3x+1}{4}\hfill \\ y=3x+2\hfill \end{array}$

$\begin{array}{l}x=4\\ y=\mathrm{-3}\end{array}$

$\left(5,4\right)$ and $\left(7,9\right)$

$\left(\mathrm{-3},2\right)$ and $\left(4,\mathrm{-7}\right)$

$\left(\mathrm{-5},4\right)$ and $\left(2,4\right)$

$\left(\mathrm{-1},\mathrm{-2}\right)$ and $\left(3,4\right)$

$\left(3,\mathrm{-2}\right)$ and $\left(3,\mathrm{-2}\right)$

$\begin{array}{l}\left(\mathrm{-1},3\right)\text{ and }\left(5,1\right)\\ \left(\mathrm{-2},3\right)\text{ and }\left(0,9\right)\end{array}$

$\begin{array}{l}\left(2,5\right)\text{ and }\left(5,9\right)\\ \left(\mathrm{-1},\mathrm{-1}\right)\text{ and }\left(2,3\right)\end{array}$

$0.537x-2.19y=100$

$\mathrm{4,500}x-200y=\mathrm{9,528}$

$\frac{200-30y}{x}=70$

Starting with the point-slope formula $y-y_1=m(x-x_1),$ solve this expression for $x$ in terms of $x_1,y,y_1,$ and $m.$

Starting with the standard form of an equation $\text{A}x\text{ + B}y\text{ = C,}$ solve this expression for y in terms of $A,B,C,$ and $x.$ Then put the expression in slope-intercept form.

Use the above derived formula to put the following standard equation in slope intercept form: $7x-5y=25.$

Given that the following coordinates are the vertices of a rectangle, prove that this truly is a rectangle by showing the slopes of the sides that meet are perpendicular.

$(\mathrm{-1},1),(2,0),(3,3)\text{,}$ and $(0,4)$

Find the slopes of the diagonals in the previous exercise. Are they perpendicular?

The slope for a wheelchair ramp for a home has to be $\frac{1}{12}.$ If the vertical distance from the ground to the door bottom is 2.5 ft, find the distance the ramp has to extend from the home in order to comply with the needed slope.

If the profit equation for a small business selling $x$ number of item one and $y$ number of item two is $p=3x+4y,$ find the $y$ value when $p=\text{\$}453\text{ and }x=75.$

What is your cost if you travel 50 mi?

If your cost were $\text{\$}63.75,$ how many miles were you charged for traveling?

Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?