1. Slope of given line = -1/2
2. Slope of line parallel to given line = -1/2
3. Slope of line perpendicular to given line = 2
Step-by-step explanation:
1. Slope of Given line:
We can see that there are two points on the line(highlighted by dots)
Let the two points be (x1,y1) and (x2,y2)
Then
(x1,y1) = (2,2)
(x2,y2) = (-2,4)
The formula for slope is given by:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Putting the values
[tex]m = \frac{4-2}{-2-2}\\m = \frac{2}{-4}\\m = -\frac{1}{2}[/tex]
Hence, the slope of given line is -1/2
2. Slope of line parallel to given line
Let [tex]m_1[/tex] be the slope of the line parallel to given line.
The slopes of two parallel lines are equal as they change at same rate with respect to x-axis.
So,
[tex]m = m_1\\-\frac{1}{2} = m_1[/tex]
Hence,
The slope of line parallel to given line will also be -1/2
3. Slope of line perpendicular to given line:
Let m_2 be the slope of line perpendicular to given line
The slope of line perpendicular to a given line is the negative reciprocal of the slope of first line or simple it can be put like " The product of slopes of two perpendicular lines is -1"
So,
[tex]m.m_2 = -1\\-\frac{1}{2}.m_2 = -1\\m_2 = -1 * -2\\m_2 =2[/tex]
Hence,
The slope of line perpendicular to given line is: 2
Keywords: slope, parallel lines
Learn more about parallel lines at:
- brainly.com/question/5059091
- brainly.com/question/5069437
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