help meeeee<3?

Question

1. Which of the following statements about parallel lines is NOT correct?

Parallel lines have the same slope

Parallel lines do not intersect ever.

Parallel lines have one point in common and thus have only one solution.

Parallel lines are an equal distance apart at all times.

2. Which of the following equations represent perpendicular lines?

y = ½x + 3
y = -2x - 2

y = 2x + ¼
y = 2x - 4

y = 2x + 4
y = ½x - 2

2x + 3y = 6
-½x + 4y = 8

3. 6x - 2y = 24
The slope of this line is _____?

4. 6x - 2y = -24
The y-intercept of this equation is ____?

5. y = -½x + 4
A line that is perpendicular to this line would have a slope equal to ____?

6. y = 4x - 2
A line that is parallel to this line would have a slope of ______?

7. Perpendicular lines have negative reciprocal slopes, so if one line has the slope of ¼, the other line will have the slope equal to -4
true or false?


8. Use the substitution method for this system of equations:

y = ½x + 4
2x + 4y = 8

(2,5)
(-2,3)
(0,2)
(4,0)

Answer 1

1. Parallel lines have the same slope. (m)
m1 = m2

2. Perpendicular must have a negative reciprocal slope.
m = -1/m

y = ½x + 3 ---------------------> m = 1/2
y = -2x - 2 -------------------->m = -2

3. 6x - 2y = 24

Put into y = mx + b form to get the slope (m).

6x - 2y = 24
-2y = -6x + 24
y = 3x - 12
m = 3 your slope.

4. 6x - 2y = -24

Put into y = mx + b form to find y-intercept (b).

6x - 2y = -24
-2y = -6x - 24
y = 3x + 12
b = 12 your y-intercept. When x = 0----------->(0, 12)

5. Perpendicular to this line? Once again "negative reciprocal".... m = -1/m

y = -½x + 4
m = -1/2
So:
m = 2

6. Parallel to this line? "same slope" m = m
y = 4x - 2
m = 4
So:
m = 4

7. true
m = -1/m
-4 = 1/4

8. Use substitution method:
So insert that first equation into the "y" of the second equation.

y = ½x + 4
2x + 4y = 8

2x + 4(½x + 4) = 8
2x + 2x + 16 = 8
4x + 16 = 8
4x = 8 - 16
4x = -8
x = -2

NOW, take that x and insert it into the first equation above to find y.

y = ½x + 4
y = ½(-2) + 4
y = -1 + 4
y = 3

So putting these together: (x, y) = (-2, 3)

Answer 2

1. Parallel lines never intersect, so they have no point(s) in common.
2. Perpendicular lines have slopes which are opposite recripicals of each other. In this case, the first equation is right.
3. The equation for a slope of a line is: y = mx + b. Reduce this equation down, and your left with: y = 3x - 12. The slope is 3.
4. The y-intercept is the 'b' value in the slope equation. In this case, -12.
5. Perpendicular lines have a slope which is the negative recriprical. The original slope is -1/2, so it should be +2.
6. For a line to be perpendicular, you only need to have the same slope. In this case, a slope equal to 4.
7. True
8. To use the substitution method, solve either equation in terms of the other. In this case, the first equation is already solved in terms of y. Plug the "1/2x + 4" value into the second equation for Y, then solve. Once you have your X value, then place it in either equation and solve for Y.
X = -2, Y = 3

Hope that helps.

Answer 3

1. Parallel lines have one point in common and thus have only one solution.
2. y = ½x + 3
y = -2x - 2
3. Slope = 6/2 = 3
4. 24/2 = 12 = y-intercept
5.-1/(-1/2) = 2
6. 4 {parallel line have same slope]
7. True [-1/(1/4) = -4
8. 2x +4(½x + 4) = 8
2x+ 2x +16 = 8
4x = -8
x = -2 , so answer must be (-2,3)