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Algebra 1A unit 6 lesson 6
1. Write an equation in slope-intercept form of the line rhat passes through the given point and is parallele to the graph of the equation
(2,-2);y=-x-2

2. (2,-1);y=-3/2x+6

3. (4,2);x=-3

4. (-2,3);y=1/2x-1

5. (5,0);y+1=2(x-3)

6. determine whether the graphs of the given equations are parellel, perpendicular, or neither
Y=x+11
Y=-x+2

7. Y=-2x+3
Y=2x+y=7

8. Y=4x-2
-x+4y=0

9. Determine whether the statement is always, sometimes or never true
Two lines with positive slopes are parellel

10. Two lines with the same slope and different y-intercepts are perpendicular

Respuesta :

texaschic101
1. y = -x - 2...slope here is -1. A parallel line will have the same slope

y = mx + b
slope(m) = -1
(2,-2)...x = 2 and y = -2
now we sub and find b, the y int
-2 = -1(2) + b
-2 = -2 + b
-2 + 2 = b
0 = b

so ur parallel equation is : y = -x
=========================
2. -1 = -3/2(2) + b
    -1 = -3 + b
    -1 + 3 = b
     2 = b
parallel equation is : y = -3/2x + 2
==========================
3. parallel equation is : x = 4
==========================
4. 3 = 1/2(-2) + b
    3 = -1 + b
    3 + 1 = b
    4 = b
parallel equation is : y = 1/2x + 4
===========================
5. y + 0 = 2(x - 5)
    y = 2x - 10 <== parallel line
============================
6. neither
============================
7. if ur second equation is : 2x + y = 7, then the lines are parallel
============================
8. neither
============================
9. sometimes
============================
10. never
xero099

Answer:

1) [tex]y = -x[/tex], 2) [tex]y = -\frac{3}{2}\cdot x +2[/tex], 3) [tex]x = 4[/tex], 4) [tex]y = \frac{1}{2}\cdot x + 4[/tex], 5) [tex]y = 2\cdot x -10[/tex], 6) Perpendicular, 7) Neither, 8) Neither, 9) Sometimes, 10) Never true.

Step-by-step explanation:

The slope-intercept form has the following form:

[tex]y = m\cdot x + b[/tex]

Where:

[tex]y[/tex] - Dependent variable.

[tex]x[/tex] - Independent variable.

[tex]m[/tex] - Slope.

[tex]b[/tex] - Intercept.

1) The slope of the function is -1. The intercept has to be found:

[tex]-2 = -1\cdot 2 + b[/tex]

[tex]b = 0[/tex]

[tex]y = -x[/tex]

2) The slope of the function is -3/2. The intercept has to be found:

[tex]-1 = -\frac{3}{2}\cdot 2 + b[/tex]

[tex]b = 2[/tex]

[tex]y = -\frac{3}{2}\cdot x +2[/tex]

3) The slope of the function is undefined. (Vertical line) The function is equal to:

[tex]x = 4[/tex]

4) The slope of the function is 1/2. The intercept has to be found:

[tex]3 = \frac{1}{2}\cdot (-2)+b[/tex]

[tex]b = 4[/tex]

[tex]y = \frac{1}{2}\cdot x + 4[/tex]

5) This expression has a point-slope form. The slope of the function is 2. The intercept has to be found:

[tex]0 = 2\cdot (5) + b[/tex]

[tex]b = -10[/tex]

[tex]y = 2\cdot x -10[/tex]

6) The functions [tex]y = x + 11[/tex] and [tex]y = -x +2[/tex] have different slopes and observe the relationship of [tex]m = -\frac{1}{n}[/tex]. Both equations are perpendicular to each other.

7) The functions [tex]y = -2\cdot x + 3[/tex] and [tex]x = \frac{7}{2}[/tex] have different slope and do not observe the relationship of [tex]m = -\frac{1}{n}[/tex]. Both equations are not perpendicular nor parallel to each other.

8) The functions [tex]y = 4\cdot x - 2[/tex] and [tex]y = \frac{1}{4}\cdot x[/tex] have different slope and do not observe the relationship of [tex]m = -\frac{1}{n}[/tex]. Both equations are not perpendicular nor parallel to each other.

9) Sometimes. Two lines with positive slopes are parallel if and only if each one has the same slope.

10) Never true. Two lines with different y-intercepts that are supposed to be perpendicular must observe the following relationship in their slopes: [tex]m = -\frac{1}{n}[/tex]. Slopes must be distinct.

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