### All Algebra II Resources

## Example Questions

### Example Question #1 : Transformations Of Linear Functions

Write the equation from the augmented matrix.

**Possible Answers:**

**Correct answer:**

Do the first row first and use x and y to represent your variable.

### Example Question #1 : Transformations Of Linear Functions

Solve for in the equation.

**Possible Answers:**

**Correct answer:**

Solve for x by isolating the variable.

### Example Question #1 : Transformations Of Linear Functions

What is the equation of the line that intersects the point and ?

**Possible Answers:**

**Correct answer:**

We are only given the points the line intersects. This can be used to find the slope of the line, knowing that slope is rise/run, or change in /change in or by the formula,

.

By substituting, we get

for the slope.

To find the intercept, we can use the equation , where ---> .

Since both given points are on the line, either can be used to solve for :

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### Example Question #4 : Transformations Of Linear Functions

Which line is perpendicular to the line ?

**Possible Answers:**

**Correct answer:**

Lines that are perpendicular have negative reciprocal slopes. Therefore, the line perpendicular to must have a slope of . Knowing that the slope of is , only has a slope of .

### Example Question #5 : Transformations Of Linear Functions

Which line would never intersect a line with the slope ?

**Possible Answers:**

**Correct answer:**

This question is very simple once you realize that a line that will never intersect another line must have the same slope (parallel lines will never intersect). Therefore you must look for the choice that has a slope of . Each answer can be converted to the form or by knowing that in the equation , the slope of the line is simply . In the correct answer, , the slope would be , which simplfies to .

*Note* the y-intercept is irrelevant to finding the correct answer.

### Example Question #6 : Transformations Of Linear Functions

If the equation was shifted left three units and up one unit, what is the new equation of the line?

**Possible Answers:**

**Correct answer:**

If the equation shifts left three units, the term will become .

The equation shifting up one unit will change the y-intercept of the equation.

Rewrite the equation and distribute to simplify.

The correct equation is:

### Example Question #7 : Transformations Of Linear Functions

Write the equation of a line that is parallel and two points lower than the line .

**Possible Answers:**

**Correct answer:**

Straight-line equations may be written in the slope-intercept form: .

In this form, equals the slope of the line and corresponds to the y-intercept.

The given line has a slope of and a y-intercept of positive . A line that is parallel to another has the same slope. Therefore, the slope of the new line will have to be .

In order to shift a line down, you must change the y-intercept. Since we are moving the line down by the y-intercept should be because .

If we plug those values into the slope-intercept equation, then we have the answer: .

### Example Question #8 : Transformations Of Linear Functions

Given the equation , which of the following lines are steeper?

**Possible Answers:**

None of these.

**Correct answer:**

Considering that slope (m) is defined as rise over run, you can look that the fractional slopes and determine which are steeper or more flat. For example, is equivalent to up one and over 8 while is equivalent to up one and over 10. As you can see the slope of the second line "runs" horizontally more than does the first slope and is therefore flatter. Based on this fact one can conclude that the larger the the slope, the steeper the line. So select the largest slope and this is the steepest line. In our case it is because is steeper (larger) than (flatter and a smaller number).

### Example Question #9 : Transformations Of Linear Functions

The equation is shifted eight units downward. Write the new equation.

**Possible Answers:**

**Correct answer:**

Rewrite the equation in slope-intercept format, .

Subtract two on both sides.

If the equation shifts eight units down, this means that the y-intercept, , would also subtracted eight units.

The correct answer is:

### Example Question #1 : Transformations Of Linear Functions

Which of the following describes the transformation of the function from its parent function ?

**Possible Answers:**

Stretched vertically by a factor of 2 and translated 3 units up

Stretched vertically by a factor of 2 and translated 3 units to the right

Stretched vertically by a factor of 2 and translated 3 units down

Stretched vertically by a factor of 2 and translated 3 units to the left

**Correct answer:**

Stretched vertically by a factor of 2 and translated 3 units to the right

The only differences among the answer choices is the translation. The translation of a function is determined by , which represents a horizontal translation *h* units to the right and *k* units up. In this case, *h* = 3 and *k* = 0, which indicates a translation 3 units to the right.