Chapter 3

Use intercepts and a checkpoint to graph equation. \(2 x-3 y=-11\)

Write each sentence as a linear inequality in two variables. Then graph the inequality. The difference between 5 times the \(x\) -variable and 2 times the \(y\) -variable is at most 10

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

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 equation. \(3 x-2 y=-7\)

Write each sentence as a linear inequality in two variables. Then graph the inequality. The sum of 4 times the \(x\) -variable and 2 times the \(y\) -variable is at most 8

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

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. $$2 x+y=0$$

Write each sentence as a linear inequality in two variables. Then graph the inequality. The \(y\) -variable is no less than \(\frac{1}{2}\) of the \(x\) -variable.

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

Describe how to write the equation of a line if its slope and a point on the line are known.

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 \(y\)

Write each sentence as a linear inequality in two variables. Then graph the inequality. The \(y\) -variable is no less than \(\frac{1}{4}\) of the \(x\) -variable.

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

Describe how to write the equation of a line if two points on the line are known.

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. $$4 y=5 x$$

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

Write each sentence as a linear inequality in two variables. Then graph the inequality. The \(y\) -variable is no more than \(-1\)

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

I use \(y=m x+b\) to write equations of lines passing through two points when neither contains the \(y\) -intercept.

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. $$2 x+y=3$$

The line passing through \((-1, y)\) and \((1,0)\) is perpendicular to the line joining \((2,3)\) and \((-2,1) .\) Find \(y\)

Write each sentence as a linear inequality in two variables. Then graph the inequality. The \(y\) -variable is no more than \(-2\)

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

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. In many examples, I use the slope-intercept form of a line's equation to obtain an equivalent equation in point-slope form.

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. $$3 x+y=4$$

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. $$x+3 y=0 \quad(0,0),\left(1, \frac{1}{3}\right),\left(2,-\frac{2}{3}\right)$$

Determine whether each statement "makes sense" or "does not make sense" and explain your reasoning. I have linear models that describe changes for men and women over the same time period. The models have the same slope, so the graphs are parallel lines, indicating that the rate of change for men is the same as the rate of change for women

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. $$x+5 y=0 \quad(0,0),\left(1, \frac{1}{5}\right),\left(2,-\frac{2}{5}\right)$$

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. $$5 x+3 y=15$$

Graph equation. \(y=4\)

Many elevators have a capacity of 2000 pounds. a. If a child averages 50 pounds and an adult 150 pounds, write an inequality that describes when \(x\) children and \(y\) adults will cause the elevator to be overloaded. b. Graph the inequality. Because \(x\) and \(y\) must be nonnegative, limit the graph to quadrant I and its boundary only. c. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?

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

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 equation. \(y=2\)

A patient is not allowed to have more than 330 milligrams of cholesterol per day from a diet of eggs and meat. Each egg provides 165 milligrams of cholesterol. Each ounce of meat provides 110 milligrams of cholesterol. a. Write an inequality that describes the patient's dietary restrictions for \(x\) cggs and \(y\) ounces of meat. b. Graph the inequality. Because \(x\) and \(y\) must be nonnegative, limit the graph to quadrant I and its boundary only. c. Select an ordered pair satisfying the inequality. What are its coordinates and what do they represent in this situation?

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

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The line whose equation is \(y-3=7(x+2)\) passes through \((-3,2).\)

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 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. $$y=12 x$$

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

The grade of a road or ramp refers to its slope expressed as a percent. Use this information to solve Exercises \(49-50\). Construction laws are very specific when it comes to access ramps for the disabled. Every vertical rise of 1 foot requires a horizontal run of 12 feet. What is the grade of such a ramp? Round to the nearest tenth of a percent. (GRAPH CANT COPY)

Graph equation. \(y=-3\)

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. $$y=14 x$$

Graph both linear equations in the same rectangular coordinate system. If the lines are parallel or perpendicular, explain why. $$\begin{aligned}&y=-2 x+1\\\&y=2 x+1\end{aligned}$$