Chapter 7

For the following problems, construct a coordinate system and graph the inequality. $$ -6 x+4>-14 $$

Solve the following inequalities by graphing. $$ -3 x+2 y \leq 4 $$

Find the equation of each line given the following information. Use the slope- intercept form as the final form of the equation. $$ m=5, y \text { -intercept }(0,8) $$

Use the \(y\) -intercept and the slope to graph each line. $$ y=\frac{-2}{3} x+4 $$

The following equation are in slope-intercept form. In each case, specify the slope and \(y\) -intercept. $$ y=2 x+7 ; \quad m=\quad b= $$

Graph \(3 x+y=3\) using the intercept method.

Plot the ordered pairs. $$ (1,3),(4,-5),(0,1),(-4,0) $$.

Graph the equation \(4 x+1=-7\).

Graph the equations and inequalities. $$ 4 x-3=-7 $$

For the following problems, construct a coordinate system and graph the inequality. $$ -8

Solve the following inequalities by graphing. $$ x-4 y<4 $$

Find the equation of each line given the following information. Use the slope- intercept form as the final form of the equation. $$ m=-8, y \text { -intercept }(0,3) $$

Use the \(y\) -intercept and the slope to graph each line. $$ y=\frac{3}{4} x $$

The following equation are in slope-intercept form. In each case, specify the slope and \(y\) -intercept. $$ y=-4 x+2 ; \quad m=\quad b= $$

Plot the following ordered pairs. $$ (8,2),(10,-3),(-3,10),(0,5),(5,0),(0,0),\left(-7,-\frac{3}{2}\right) $$

Graph the inequality \(3 x \leq 18\).

Plot the ordered pairs (3,1),(-2,4),(0,5),(-2,-2) .

Solve the following inequalities by graphing. $$ 3 x+y>0 $$

Find the equation of each line given the following information. Use the slope- intercept form as the final form of the equation. $$ m=2, y \text { -intercept }(0,-7) $$

Graph the equations. $$ y=\frac{2}{3} x+1 $$

The following equation are in slope-intercept form. In each case, specify the slope and \(y\) -intercept. $$ y=-5 x-1 ; \quad m=\quad b= $$

$$ x+2 y=6 $$

Graph the inequality \(-3 m+1<13\).

Solve the following inequalities by graphing. $$ x \geq 1 $$

Graph the equations. $$ y=\frac{1}{4} x-2 $$

The following equation are in slope-intercept form. In each case, specify the slope and \(y\) -intercept. $$ y=\frac{2}{3} x-10 ; \quad m=\quad b= $$

Using ordered pair notation, what are the coordinates of the origin?

Graph the inequality \(-3 \leq x-5<5\).

What is the geometric structure of the graph of all the solutions to the equation \(2 y+3 x=-4 ?\)

Solve the inequalities by graphing. $$ y

Find the equation of each line given the following information. Use the slope- intercept form as the final form of the equation. $$ m=-1, y \text { -intercept }(0,-10) $$

Graph the equations. $$ y=5 x-4 $$

The following equation are in slope-intercept form. In each case, specify the slope and \(y\) -intercept. $$ y=\frac{-5}{8} x+\frac{1}{2} ; \quad m=\quad b= $$

Graph \(y=2\).

We know that solutions to linear equations in two variables can be expressed as ordered pairs. Hence, the solutions can be represented as points in the plane. Consider the linear equation \(y=\) \(2 x-1\). Find at least ten solutions to this equation by choosing \(x\) -values between -4 and 5 and computing the corresponding \(y\) -values. Plot these solutions on the coordinate system below. Fill in the table to help you keep track of the ordered pairs.

Graph the linear equation \(-6 y=480\).

In what form is the linear equation in two variables \(a x+b y=c ?\)

Solve the inequalities by graphing. $$ x+y \leq 1 $$

Find the equation of each line given the following information. Use the slope- intercept form as the final form of the equation. $$ m=4, \text { the point }(5,2) $$

Graph the equations. $$ y=-\frac{6}{5} x-3 $$

The following equation are in slope-intercept form. In each case, specify the slope and \(y\) -intercept. $$ y=-3 x ; \quad m=\quad b= $$

Graph \(x=-4\)

Graph the linear equations and inequalities. $$ 4 x+7=19 $$

Graph the equations and inequalities. $$ 3 x+4 \leq 12 $$

In what form is the linear equation in two variables \(y=m x+b ?\)

Solve the inequalities by graphing. $$ -x+2 y+4 \geq 0 $$

Find the equation of each line given the following information. Use the slope- intercept form as the final form of the equation. $$ m=-6, \text { the point }(-1,0) $$

Graph the equations. $$ y=\frac{3}{2} x-5 $$

Graph the linear equations and inequalities. $$ 8 x-1=7 $$

Graph the equations and inequalities. $$ -16 \leq 5 x-1 \leq-11 $$