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jenyasd209 [6]
3 years ago
12

Write an equation of the line that passes through the point (-4,-1) and is parallel and perpendicular to the line 2x+7y=14

Mathematics
1 answer:
Darina [25.2K]3 years ago
3 0

Answer: Parallel: y=-2/7x-2 1/7 Perpendicular: y=7/2x+13

Step-by-step explanation:

2x+7y=14

Subtract 2x from both sides.

7y=-2x+14

Divide both sides by 7 to isolate y.

y=-2/7x+2

Parallel:

Plug in x and y with same slope as the original.

-1=-2/7(-4)+b

Solve for b:

-1=8/7+b

-2 1/7=b

y=-2/7x-2 1/7

Perpendicular:

Plug in x and y with the negative inverse of the original slope.

-1=7/2(-4)+b

Solve for b.

-1=-28/2+b

-1=-14+b

13=b

y=7/2x+13

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as the union of 2 different intervals say a and b.

Let a be the interval containing the smallest value.

Then the smallest value of a is -5, and the largest possible value of a is 0, not included, if we want to write a as an interval, without "gaps", or "holes".

So a=[-5, 0)

similarly, b=(0, 4).


Answer: [-5, 4)=[-5, 0)∪(0, 4)

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Find the distance between 2 3/5 and -1 on a number line
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write the equation in slope-intercept form of the line that has a slope of -3 and contains the point (4, -5).
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You can answer this question by plugging the given values into point-slope form, which is y - y_{1} = m (x - x_{1}). M will represent slope and x_{1} and y_{1} will represent the x and y coordinates.

   y - y_{1} = m (x - x_{1})   Substitute in the values
y - (-5) = 4 (m - 4)   Cancel out the -(-5)
   y + 5 = 4 (m - 4)   Use the Distributive Property
   y + 5 = 4m - 16    Subtract 5 from both sides
       
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\longrightarrow{\mathfrak{\frac{-9}{6}÷\frac{3}{-2}}}

\longrightarrow{\sf{\frac{-\cancel{9}}{\cancel{6}}\times\frac{-\cancel{2}}{\cancel{3}}}}

\longrightarrow{\sf{\frac{3}{3}}}

\longrightarrow{\boxed{\bf{1}}}

Identity applied -

\star{\:\:\:\:\:\:\boxed{\bf{\frac{a}{b}÷\frac{c}{d}=\frac{a}{b}\times\frac{d}{c}}}}

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