1. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is [tex]\frac{-5}{2}[/tex]
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = [tex]\frac{1}{2}[/tex] x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = [tex]\frac{-2}{5}[/tex] x - 2
Step-by-step explanation:
Let us revise some rules
1.
∵ The equation of the line is 5y = 10 + 2x
- Put the equation in the form of slope-intercept
- Divide both sides by 5
∴ y = 2 + [tex]\frac{2}{5}[/tex] x
∴ m = [tex]\frac{2}{5}[/tex]
∴ The slope of the line is [tex]\frac{2}{5}[/tex]
∵ The product of the slopes of the perpendicular lines is -1
- That means if the slope of a line is m, then the slope of the
perpendicular line to this line is [tex]\frac{-1}{m}[/tex]
∵ The slope of the line = [tex]\frac{2}{5}[/tex]
∴ The slope of the perpendicular line [tex]\frac{-5}{2}[/tex]
The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is [tex]\frac{-5}{2}[/tex]
2.
∵ Line a is represented by the equation y = -2x + 3
∴ m = -2
∴ The slope of the line is -2
∵ The equation of the line is y = 2x - 1
∴ m = 2
∴ The slope of the line is 2
∵ 2 ≠ -2
∵ 2 × -2 ≠ -1
∴ The two lines neither parallel nor perpendicular
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
∵ The equation of the line is y = -2x + 5
∴ m = -2
∴ The slope of the line is -2
∵ The slopes of the lines are equal
∴ The two lines are parallel
The line y = -2x + 5 is parallel to the line y = -2x + 3
∵ The equation of the line is y = [tex]\frac{1}{2}[/tex] x + 7
∴ m = [tex]\frac{1}{2}[/tex]
∴ The slope of the line is [tex]\frac{1}{2}[/tex]
∵ [tex]\frac{1}{2}[/tex] × -2 = -1
∵ The product of the slopes of the lines is -1
∴ The two lines are perpendicular
The line y = [tex]\frac{1}{2}[/tex] x + 7 is perpendicular to the line
y = -2x + 3
3.
∵ The equation of a line that is parallel to the line whose equation
is 2x + 5y = 10
∴ Their slopes are equal
- Put the equation in the form of y = mx + b to find m
∵ 2x + 5y = 10
- Subtract 2x from both sides
∴ 5y = 10 - 2x
- Divide both sides
∴ y = 2 - [tex]\frac{2}{5}[/tex] x
∴ m = [tex]\frac{-2}{5}[/tex]
∴ The slope of the line is [tex]\frac{-2}{5}[/tex]
∵ The form of the equation is y = mx + b
∵ m = [tex]\frac{-2}{5}[/tex]
∴ y = [tex]\frac{-2}{5}[/tex] x + b
∵ The line passes through the point (5 , -4)
- Substitute the coordinates of the point in the equation to find b
∵ x = 5 , y = -4
∴ -4 = [tex]\frac{-2}{5}[/tex] (5) + b
∴ -4 = -2 + b
- Add 2 to both sides
∴ -2 = b
∴ y = [tex]\frac{-2}{5}[/tex] x - 2
The equation of a line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = [tex]\frac{-2}{5}[/tex] x - 2
Learn more:
You can learn more about the equation of a line in brainly.com/question/4152194
#LearnwithBrainly
here is your answer!
1. The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
2.
The line y = 2x - 1 is neither parallel nor perpendicular to the line
y = -2x + 3
The line y = -2x + 5 is parallel to the line y = -2x + 3
The line y = x + 7 is perpendicular to the line
y = -2x + 3
3. The equation of the line that passes through the point (5 , -4) and
is parallel to the line whose equation is 2x + 5y = 10 is
y = x - 2
have a good day
