Question

Write the equation of a line that is perpendicular to the given line and that passes through the given point.

–3x – 6y = 17; (6, 3)


y = x – 9


y = 2x – 9


y = –2x – 9


y = x + 0
3.
Is the relationship shown by the data linear? If so, model the data with an equation.
x
y
1
5
5
10
9
15
13
20





The relationship is linear; y – 5 = (x – 1).


The relationship is not linear.


The relationship is linear; y – 5 = (x – 1).


The relationship is linear; y – 1 = (x – 5).
Write an equation in point-slope form for the line through the given point with the given slope.

(–10, –1); m =


y + 10 = (x + 1)


y – 1 = (x – 10)


y – 1 = (x + 10)


y + 1 = (x + 10)
5.
Write an equation for each translation of .

6.5 units up



y + 6.5 = | x |


y = | 6.5 x |


y = | x | + 6.5


y = | x | – 6.5
6.
Write an equation for each translation of .

5.5 units right



y = | x | + 5.5


y = | x – 5.5 |


y = | x | – 5.5


y = | x + 5.5 |
7.
Which equation translates y = | x | by 8 units to the left?


y = | x | – 8


y = | x | + 8


y = | x – 8|


y = | x + 8|

Answer 1

1. y=2x-9

5. y = | x | + 6.5

6. y = | x – 5.5 |

7. y = | x + 8|

Explanation:

There is not enough given information for some of the problems. Here are the solutions and reasons for those that area solvable:

Write a perpendicular line to the equation -3x-6y=17 by finding its slope and then flipping it to the negative reciprocal:

So -3x-6y=17 becomes y=-1/2x-17/6 where m = -1/2. The perpendicular slope is 2.

Using the point given, write the equation in point slope form and simplify to the slope intercept form:

`y-y_1=m(x-x_1)\\y-3=2(x-6)\\y-3=2x-12\\y=2x-9`

When translating functions, remember:

• Shifting left or right is addition and subtraction respectfully inside the function.
• Shifting up and down is addition and subtraction respectfully outside the function.

5. A translation of 6.5 units up is +6.5 outside the function y=|x| so equation y=|x|+6.5 is the translation.

6. A translation of 5.5 units to the right is - 5.5 inside the function y=|x| so equation y=|x-5.5| is the translation.

7. A translation of 8 units to the left is +8 inside the function y=|x| so equation y=|x+8| is the translation.