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3 years ago

the line passing through point (4, -1) and perpendicular to the line whose equation is 2x - y - 7 = 0

Mathematics

1 answer:

ch4aika [34]3 years ago

7 0

Answer:

y = -x/2 + 1

Step-by-step explanation:

Step 1: find the slope

2x - y - 7 = 0

2x - 7 = y

y = 2x - 7

Equation of a line is y = mx + c

m = slope

m = 2

Note: if two lines are perpendicular to the other, both lines are negative reciprocal of each other

Therefore m = -1/2

Step 2: using a point slope form

y - y1 = m( x - x1)

( 4 , -1)

x = 4

y = -1

y - (-1) = -1/2(x - 4)

y + 1 = -1/2(x - 4)

Open the bracket

y + 1 = -x + 4 / 2

y = (-x + 4) / 2 - 1

LCM = 2

y = -x + 4 - 2 / 2

y = (-x + 2)/2

Separate the two, so as to get the slope and the intercept

y = -x/2 + 2/2

y = -x/2 + 1

The equation of the line is

y = -x/2 + 1

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Need help ASAP please help me

pentagon [3]

Answer:

Part 1) $x+2.25=6.50$

Part 2) $s+2.25=6.50$

Part 3) $25w=600$

Part 4) $\frac{1}{4}d=1.5$

Part 5) $7.25h=87$

Part 6) $\frac{1}{2}x=63.75$

Part 7) see the explanation

Part 8) see the explanation

Step-by-step explanation:

Part 1)

Let

x ----> the amount that Jackson spent on his lunch

we know that

The amount that Jackson spent on his lunch plus $2.25 is equal to the amount that Matt spent on his lunch

The linear equation that represent this situation is

$x+2.25=6.50$

$x=\$4.25$

Part 2)

Let

s ----> the number of seats in gymnasium

we know that

The number of seats in gymnasium minus 112 is equal to the number of seats in auditorium

The linear equation that represent this situation is

$s-112=600$

$s=712\ seats$

Part 3)

Let

w ----> the number of weeks

we know that

The number of weeks multiplied by $25 per week must be equal to $600

The linear equation that represent this situation is

$25w=600$

$w=24\ weeks$

Part 4)

Let

d -----> distance that Carolyn ran

we know that

One fourth the distance that Carolyn ran is equal to the distance that Erin ran

The linear equation that represent this situation is

$\frac{1}{4}d=1.5$

$d=6\ miles$

Part 5)

Let

h ----> the number of hours worked at the grocery store

we know that

The number of hours worked multiplied by $7.25 per hour must be equal to $87

The linear equation that represent this situation is

$7.25h=87$

$h=12\ hours$

Part 6)

Let

x -----> Emilio's savings

we know that

One half of Emilio's savings is equal to $63.75

The linear equation that represent this situation is

$\frac{1}{2}x=63.75$

$x=\$127.50$

Part 7) we have

$14x=21$

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Ben earns $14 per hour in the forex market. In how many hours he will have earned $21?

Part 8) we have

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Let

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