Algebra Chap 3 review

Determine whether the equation is linear or not. If yes, write the equation in standard form y = 2 − 3x

Yes. 3x + y = 2

Look at the graph for problem #7 on page 198. Write an equation for the graph in function notation

f(x) = 3x − 2

Look at the graph for problem #3 on page 198. Write an equation for the graph in function notation

f(x) = −x + 3

Find the value of r so the line that passes through each pair of points has the given slope. (r, 3), (5, 9), m = 2

r = 2

Find the value of r so the line that passes through each pair of points has the given slope. (−4, 3)), (r, 5), m= 1/4

r = 4

Solve the equation 4x − 1 = 0

x = 1/4

Solve the equation 0 = 4 − 2x

x = 2

Graph 2x + 4y = 16 using x an y intercepts

x intercept is 8, and the y intercept is 4. See page 155 and 156 to check the work and graph

Graph 2x + y = −2 using the x and y intercepts

x intercept is −1 and the y intercept is −2

Which of the following equations is a direct variation equation? y = x + 2 or y = 3x

y = 3x because it is of the form y = kx

What is the general equation for a direct variation equation?

y = kx

Find the slope of the line that passes through (10, 0) and (−2, 4)

−1/3

Look at problem 16 on page 176. You will see a graph. What is the slope of the graph?

−4/3

What point does every direct variation equation go through?

(0, 0)

Define slope

(y2 − y1)/(x2 − x1) Other definitions are rise/run and change in y/change in x

Find the slope of the line that passes through (6, 1) and (−6, 1)

0

Look at problem 17 on page 176. You will see a graph. What is the slope of the graph?

1/2

Find the next three terms of the arithmetic sequence 22, 20, 18, 16 ...

14, 12, 10

y = 2x The constant of variation is _________

2

y = 2x The slope is ____________

2

Find the next three terms of the arithmetic sequence 3.1, 4.1, 5.1, 6.1 ...

7.1, 8.1, 9.1

Solve the equation 15x −30 = 5x − 50 by graphing and algebraically

Graph f(x) = 10x + 20 and it crosses the x-axis at − 2. Solve 10x + 20 and x = −2

Determine whether the equation is linear or not. If yes, write the equation in standard form y = 3x² + 1

No, because the x is raised to a power greater than one

Determine whether the equation is linear or not. If yes, write the equation in standard form xy = 6

No, because variables are multiplied together

Graph y − x = 4 using a table

Solve the equation for y. y = x + 4. Some points on the line are (0, 4), (1, 5), (−1, 3)

Graph y = −6x

Some points on the line are (0, 0), (1, −6),(−1, 6) See page 181 for a picture of the graph

Graph y = 1/3 x + 2 using a table

Some points on the line are (0, 2),(3, 3), (6, 4). Check page 156 to see the graph.

Suppose y varies directly as x. Write a direct variation equation that relates x and y. Solve. If y = 7.5 when x = .5, find y when x = −0.3.

The equation is y = 15x. The value for y is −4.5

Suppose y varies directly as x. Write a direct variation equation that relates x and y. Then solve. If y = −4 when x = 2, find y when x = −6.

The equation is y = −2x. The value for y is 12

Write an equation for the nth term of the arithmetic sequence 7, 13, 19, 25 ...

The nth term = 6n + 1

Write an equation for the nth term of the arithmetic sequence 30, 26, 22, 18 ....

The nth term = −4n + 34

Find the slope of the line that passes through (5, 2) and (5, −2)

Undefined

Look at problem 11 on page 183. Name the constant of variation. What is the slope?

Constant of variation is −5 The slope is −5

Is the following an arithmetic sequence 1, 4, 9, 16...

No. There is not a common difference.