Chapter 3

Use intercepts and a checkpoint to graph each equation. $$2 x+y=0$$

In which quadrants do the \(x\) -coordinates and the \(y\) -coordinates have opposite signs?

The equation of a line is given. Find the slope of a line that is a. parallel to the line with the given equation; and b. perpendicular to the line with the given equation. $$4 x+y=7$$

In Exercises \(27-38,\) graph each linear equation using the slope and y-intercept $$y=-\frac{5}{3} x$$

On the same set of axes, draw lines passing through the origin with slopes \(-1,-\frac{1}{2}, 0, \frac{1}{3},\) and 2.

Use intercepts and a checkpoint to graph each equation. $$y-3 x=0$$

Determine whether each ordered pair is a solution of the given equation. $$y=3 x \quad(2,3),(3,2),(-4,-12)$$

The equation of a line is given. Find the slope of a line that is a. parallel to the line with the given equation; and b. perpendicular to the line with the given equation. $$8 x+y=11$$

In Exercises \(27-38,\) graph each linear equation using the slope and y-intercept $$y=-\frac{4}{3} x$$

On the same set of axes, draw lines with \(y\) -intercept 4 and slopes \(-1,-\frac{1}{2}, 0, \frac{1}{3},\) and 2.

Use intercepts and a checkpoint to graph each equation. $$y-4 x=0$$

Determine whether each ordered pair is a solution of the given equation. $$y=4 x \quad(3,12),(12,3),(-5,-20)$$

The equation of a line is given. Find the slope of a line that is a. parallel to the line with the given equation; and b. perpendicular to the line with the given equation. $$2 x+4 y=8$$

a. Put the equation in slope-intercept form by solving for \(y .\) b. Identify the slope and the \(y\) -intercept. c. Use the slope and y-intercept to graph the equation. $$3 x+y=0$$

Use slopes to solve Exercises \(39-40\). Show that the points whose coordinates are \((-3,-3)\) \((2,-5),(5,-1),\) and \((0,1)\) are the vertices of a four-sided figure whose opposite sides are parallel. (Such a figure is called a parallelogram.)

Use intercepts and a checkpoint to graph each equation. $$2 x-3 y=-11$$

Determine whether each ordered pair is a solution of the given equation. $$y=-4 x \quad(-5,-20),(0,0),(9,-36)$$

The equation of a line is given. Find the slope of a line that is a. parallel to the line with the given equation; and b. perpendicular to the line with the given equation. $$3 x+2 y=6$$

a. Put the equation in slope-intercept form by solving for \(y .\) b. Identify the slope and the \(y\) -intercept. c. Use the slope and y-intercept to graph the equation. $$2 x+y=0$$

Use intercepts and a checkpoint to graph each equation. $$3 x-2 y=-7$$

Determine whether each ordered pair is a solution of the given equation. $$y=-3 x \quad(-5,15),(0,0),(7,-21)$$

The equation of a line is given. Find the slope of a line that is a. parallel to the line with the given equation; and b. perpendicular to the line with the given equation. $$2 x-3 y=5$$

a. Put the equation in slope-intercept form by solving for \(y .\) b. Identify the slope and the \(y\) -intercept. c. Use the slope and y-intercept to graph the equation. $$3 y=4 x$$

Use slopes to solve Exercises \(39-40\). The line passing through \((5, y)\) and \((1,0)\) is parallel to the line joining \((2,3)\) and \((-2,1) .\) Find \(y\)

Determine whether each ordered pair is a solution of the given equation. $$y=2 x+6 \quad(0,6),(-3,0),(2,-2)$$

The equation of a line is given. Find the slope of a line that is a. parallel to the line with the given equation; and b. perpendicular to the line with the given equation. $$3 x-4 y=-7$$

a. Put the equation in slope-intercept form by solving for \(y .\) b. Identify the slope and the \(y\) -intercept. c. Use the slope and y-intercept to graph the equation. $$4 y=5 x$$

Use slopes to solve Exercises \(39-40\). The line passing through \((1, y)\) and \((7,12)\) is parallel to the line joining \((-3,4)\) and \((-5,-2) .\) Find \(y .\)

Determine whether each ordered pair is a solution of the given equation. $$y=8-4 x \quad(8,0),(16,-2),(3,-4)$$

a. Put the equation in slope-intercept form by solving for \(y .\) b. Identify the slope and the \(y\) -intercept. c. Use the slope and y-intercept to graph the equation. $$2 x+y=3$$

Use slopes to solve Exercises \(39-40\). The line passing through \((-1, y)\) and \((1,0)\) is perpendicular to the line joining \((2,3)\) and \((-2,1) .\) Find \(y\).

Determine whether each ordered pair is a solution of the given equation. $$3 x+5 y=15 \quad(-5,6),(0,5),(10,-3)$$

a. Put the equation in slope-intercept form by solving for \(y .\) b. Identify the slope and the \(y\) -intercept. c. Use the slope and y-intercept to graph the equation. $$3 x+y=4$$

Use slopes to solve Exercises \(39-40\). The line passing through \((-2, y)\) and \((-4,4)\) is perpendicular to the line passing through \((-1,-2)\) and \((4,-1)\) Find \(y\).

Determine whether each ordered pair is a solution of the given equation. $$2 x-5 y=0 \quad(-2,0),(-10,6),(5,0)$$

a. Put the equation in slope-intercept form by solving for \(y .\) b. Identify the slope and the \(y\) -intercept. c. Use the slope and y-intercept to graph the equation. $$7 x+2 y=14$$

Determine whether each ordered pair is a solution of the given equation. $$x+3 y=0 \quad(0,0),\left(1, \frac{1}{3}\right),\left(2,-\frac{2}{3}\right)$$

a. Put the equation in slope-intercept form by solving for \(y .\) b. Identify the slope and the \(y\) -intercept. c. Use the slope and y-intercept to graph the equation. $$5 x+3 y=15$$

Determine whether each ordered pair is a solution of the given equation. $$x+5 y=0 \quad(0,0),\left(1, \frac{1}{5}\right),\left(2,-\frac{2}{5}\right)$$

In Exercises \(47-56,\) graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned} &y=3 x+1\\\ &y=3 x-3 \end{aligned}$$

Graph each equation. $$y=4$$

Determine whether each ordered pair is a solution of the given equation. $$x-4=0 \quad(4,7),(3,4),(0,-4)$$

In Exercises \(47-56,\) graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned} &y=2 x+4\\\ &y=2 x-3 \end{aligned}$$

Graph each equation. $$y=2$$

Determine whether each ordered pair is a solution of the given equation. $$y+2=0 \quad(0,2),(2,0),(0,-2)$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-8,-10)\) and parallel to the line whose equation is \(y=-4 x+3\)

In Exercises \(47-56,\) graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned} &y=-3 x+2\\\ &y=3 x+2 \end{aligned}$$

Graph each equation. $$y=-2$$

Find five solutions of each equation. Select integers for \(x,\) starting with \(-2\) and ending with \(2 .\) Organize your work in a table of values. $$y=12 x$$

Use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through \((-2,-7)\) and parallel to the line whose equation is \(y=-5 x+4\)