Without graphing the lines to the equations, given any two linear equations explain how you can tell if the lines of the two equ
1 answer:
To check whether the two lines are parallel or not, without using graphing, first we write them in slope intercept form , which is
Now we compare the slopes of both lines and if the slopes are equal, then the lines are parallel .
So without graphing, we can also check whether the given lines are parallel or not .
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Answer:
c = 15: The height of candle is 15 inches when it is not lit.
m = -1.6: The height of candle decreases 1.6 inches for every hour it is lit.
Step-by-step explanation:
We are given the following in the question:
Height of candle = 15 inches
This function gives the length of the candle in inches left after it was burn for t hours.
Comparing the given equation to a linear equation, we have:
where m is the slope and c is the y-intercept.
Comparing we, get
m = -1.6 and c = 15
Interpretation:
c = 15 mean the y-intercept is 15 that is he value of function when t = 0, thus, the height of candle is 15 inches when it is not lit.
m = -1.6 is the rate of change of the function when t increases by 1 unit that is the height of candle decreases 1.6 inches for every hour it is lit.
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
Step-by-step explanation:
Let us revise some rules
- The slope-intercept form of the linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept
- The slopes of the parallel lines are equal
- The product of the slopes of the perpendicular lines is -1
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 + x
∴ m =
∴ The slope of the line is
∵ 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
∵ The slope of the line =
∴ The slope of the perpendicular line
The slope of a line that is perpendicular to a line whose equation
is 5y = 10 + 2x is
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 = x + 7
∴ m =
∴ The slope of the line is
∵ × -2 = -1
∵ The product of the slopes of the lines is -1
∴ The two lines are perpendicular
The line y = 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 - x
∴ m =
∴ The slope of the line is
∵ The form of the equation is y = mx + b
∵ m =
∴ y = 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 = (5) + b
∴ -4 = -2 + b
- Add 2 to both sides
∴ -2 = b
∴ y = 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 = x - 2
Learn more:
You can learn more about the equation of a line in brainly.com/question/4152194
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