Chapter 3-Linear Equations

Graphing Linear Equations

100

In the equation y=mx+b, what do the m and b represent.

m=slope 

b=y-intercept

200

For the equation 4x-5y=3, what is the slope?

m=4/5

300

For the equation 2x = 3 - 4y, what is the y-intercept?

3/4

400

Graph the equation 4x + 3y = 6.

Change to y = -4/3x + 2 with intercepts at (0,2) and (3/2,0).

500

Graph the equations x=3 and y=-2.

x=3 is vertical at 3 on the x-axis.

y=-2 is horizontal at -2 on the y-axis.

Creating Linear Equations

100

Create the equation of a line that has slope 2 and contains the point (0,5)

y=2x+5

200

Create the equation of a line that has slope 1/2 and contains the point (-4,1)

y=1/2x+3

300

Create the equation of a line that is parallel to y=-3x+2 and contains the point (4,-5).

y=-3x+7

400

Create the equation of a line that is perpendicular to y=-3x+2 and contains the point (6,-2).

y=1/3x-4

500

Create the equation of a line that passes through the point (3, 5) and (-1, 2).

y=3/4x+11/4

Solving Systems of Equations

100

Solve the system of equations:

3x - 2y = 10

3x + 5y = 17

(7,1)

200

Solve the system of equations:

3x - 2y = 10

4x + y = 6

(2, -2)

300

Solve the system of equations:

3x - y = 2x - 7

2x + 5 = 2y - 9

Inifinite Solutions

400

2x = 11 - 6y

3y = 6 - x

No Solution

500

A theater production charges $21 for adult tickets and $15 for student tickets. If the production sold 102 tickets for its opening night and made $1,932 in ticket sales, how many of each type of tickets were sold?

67 adult tickets and 35 student tickets were sold.

Solving Systems of Inequalities

100

When you graph an inequality that is > or <, do you use dotted or solid lines?

Dotted

200

When graphing inequalities, if it is > or ≥, will you shade below the line or above the line?

above the line

300

Graph the inequality:

2x - 3y ≥ 6

Change to y ≤ 2/3x - 2

Intercepts at (0,-2) and (3,0) with a solid line, shaded below.

400

Solve the system of inequalities by graphing:

4x - 3y ≥ 10

2x ≤ y + 6

Change to y ≤ 4/3x - 3 1/3 and

y ≥ 2x - 6

Intersect at (4,2) and shaded between them on bottom left.

500

Solve the system of inequalities by graphing:

2x - 3y < 5

4x > 3 + 6y

Change to y > 2/3x - 5/3 and

y < 2/3x - 1/2

Parallel and shaded between them.

Functions

100

For f(x) = 2x - 3, find f(4)

f(4) = 5

200

For f(x) = 2x - 3 and g(x) = x² + 1, find f(g(4)).

g(4) = 4² + 1 = 17

f(17) = 2(17) - 3 = 34 - 3 = 31

f(g(4)) = 31

300

A linear function contains the points (-2, 5), (0, 10), and (2, 15).  What will y be when x is 6?  

We are increasing by 2 in the x, and 5 in the y. So the next points are (4, 20), (6, 25). So y = 25.

400

Find an equation for the linear function where f(3) = 7 and f(-1) = 5.

These two points are (3, 7) and (-1, 5).  The slope is 1/2.  The equation is y=1/2x + 11/2.

500

A plumber costs $110 for 3 hours and $160 for 5 hours.  How much would 8 hours cost?

The points are (3, 110) and (5, 160).  The slope is 50/2 = 25. 

110=25*3 + b

110-75 = 35 = b  so y = 25x + 35 is the equation and y= 25*8 + 35 = $235