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azaz1819
05.07.2019 •
Mathematics
Math what is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ? enter your answer in the box. line a is represented by the equation y=−2x+3 . how do these equations compare to line a? drag and drop the equations into the boxes to complete the table. parallel to line a perpendicular to line a neither parallel nor perpendicular to line a what is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10? enter your answer in the box what is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x/4+5? enter your answer in the box. in this diagram, which equation could you prove to be true in order to conclude that the lines are parallel? −ab=−cd −ab⋅−cd=−1 −ab⋅−dc=−1 −ab=−dc
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Ответ:
Part A. What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7?
Rewrite the equation −2y=3x+7 in the form
Here the slope of the given line is
If
is the slope of perpendicular line, then
Answer 1:![\dfrac{2}{3}](/tpl/images/0052/0452/d35bc.png)
Part B. The slope of the line y=−2x+3 is -2. Since
then lines from part A are not parallel to line a.
Since
both lines are not perpendicular to line a.
Answer 2: Neither parallel nor perpendicular to line a
Part C. The line parallel to the line 2x+5y=10 has the equation 2x+5y=b. This line passes through the point (5,-4), then
2·5+5·(-4)=b,
10-20=b,
b=-10.
Answer 3: 2x+5y=-10.
Part D. The slope of the line
is
Then the slope of perpendicular line is -4 and the equation of the perpendicular line is y=-4x+b. This line passes through the point (2,7), then
7=-4·2+b,
b=7+8,
b=15.
Answer 4: y=-4x+15.
Part E. Consider vectors
These vectors are collinear, then
Answer 5:![-\dfrac{a}{b}=-\dfrac{d}{c}.](/tpl/images/0052/0452/7de10.png)
Ответ:
(a) 2/3
(b) neither parallel nor perpendicular ; parallel; perpendicular
(c) y = (-2/5)*x - 2
(d) y = -4*x + 15
(e) -a*c = -d*b
Step-by-step explanation:
(a)
What is the slope of a line that is perpendicular to a line whose equation is −2y=3x+7 ?
First you need to rearrange the equation so that y term is isolated, in this case you should pass the -2 (which multiplies in one side) dividing to the other side.
y = (3*x + 7)/(-2)
y = (-3/2)*x + 7
The slope of any line is the term next to x, in this case -3/2
Two lines are perpendicular if the multiplication of each line slopes is equal to -1. For example, given lines y = m1*x+b1 and y = m2*x+b2 where m1 is the slope of the first line and m2 of the second one, they are perpendicular if m1*m2 = -1
In this case we should solve:
(-3/2)*m2 = -1
m2 = 2/3
(b)
Line a is represented by the equation y=−2x+3 . How do these equations compare to line a? Drag and drop the equations into the boxes to complete the table. Parallel to line a Perpendicular to line a Neither parallel nor perpendicular to line a y=2x−1, y=−2x+5, y=1/2x+7
Two lines are parallel if they have the same slope.
a's slope is -2
Any line perpendicular to a must have an slope of 1/2, so that -2*1/2 = -1
in y=2x−1 slope is 2 -> they are neither parallel nor perpendicular
in y=−2x+5 slope is -2 -> they are parallel
in y=1/2x+7 slope is 1/2 -> they are perpendicular
(c)
What is the equation of a line that passes through the point (5, −4) and is parallel to the line whose equation is 2x + 5y = 10?
Rearranging the equation:
5*y = -2*x + 10
y = (-2*x + 10)/5
y = (-2/5)*x + 2
Our equation has the form y = m*x + b where m = -2/5. In order to find b we replace the known point (5, -4) in the equation:
y = (-2/5)*x + b
-4 = (-2/5)*5 + b
-4 = -2 + b
-2 = b
Finally, y = (-2/5)*x - 2
(d)
What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x/4+5?
Calling m1 = 1/4 the slope of the known equation, we have to find a slope m2 which fulfill m1*m2 = -1. Replacing:
1/4*m2 = -1
m2 = -4
In the same way as before, we replace the point (2, 7) in the general equation form:
y = -4*x + b
7 = -4*2 + b
7 = -8 +b
15 = b
Finally, y = -4*x + 15
(e)
In this diagram, which equation could you prove to be true in order to conclude that the lines are parallel?
The slope of a line can be computed by m = (y1 - y2)/(x1 -x2) where (x1, y1) and (x2, y2) are points in the line
For the above line
(x1, y1) = (b, 0)
(x2, y2) = (0, a)
Replacing
m1 = (0 - a)/(b -0) = -a/b
For the below line
(x1, y1) = (-c, 0)
(x2, y2) = (0, -d)
Replacing
m2 = (0 - (-d) )/( (-c) - 0) = -d/c
m1 = m2, so that both lines are parallel
-a/b = -d/c
-a*c = -d*b
Ответ:
6x+6=24
6x=24-6
6x=18
6x/6=18/6
x=3