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Marianna [84]
10 months ago
7

Write an equation of a line passing through the point (4,-9) and parallel to the line 3x-6y=30

Mathematics
1 answer:
sesenic [268]10 months ago
7 0

The equation of a line in the slope intercept form is expressed as

y = mx + c

Where

m represents slope

c represents y intercept

The equation of the given line is expressed as

3x - 6y = 30

Rearranging it so that it will look like the slope intercept form, it becomes

6y = 3x - 30

Dividing both sides by 6, it becomes

6y/6 = 3x/6 - 30/6

y = x/2 - 5

Looking at the equation, slope, m = 1/2

If two lines are parallel, it means that they have equal slope. This means that the slope of the line parallel to the given line is 1/2

To determine the y intercept, c of the line passing through the point (4, - 9), we would substitute

x = 4, y = - 9 and m = 1/2 into the slope intercept equation. It becomes

- 9 = 1/2 * 4 + c

- 9 = 2 + c

c = - 9 - 2

c = - 11

By substtuting m = 1/2 and c = - 11 into the slope intercept equation, the equation of the line would be

y = x/2 - 11

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lianna [129]

Answer:

7 pizzas and 9 cans of juice

Step-by-step explanation:

The answer is 7 pizzas because if you add the 25 people plus her parents (That would be two more people) is 27. Then you have to multiply 27×2 that would equal 54. So, now you know you need 54 slices but what you is the amount of pizzas needed. The next step would be to divide 54÷8 that would equal 6.75 but you can't buy 6.75 pizzas, and you can't buy 6 pizzas because than you would leave people outside. You will need to buy 7 pizzas. It is better to have left overs than leaving people outside.

For the amount of cans would be 9 because if you add again 25 people plus her parents it would be 27. Then you multiply 27×1 that is obviously 27. The next step would be to divide 27÷3 and it would equal 9. And that is how you get your answer.

4 0
3 years ago
When a number x is multiplied by 9, the result is 63. What is the value of x?
ioda
What is the opposite of multiply? division. 63÷9=7
7 is your answer
4 0
2 years ago
Read 2 more answers
The graph of a linear relationship passes
Evgen [1.6K]

Answer:

The equation of the linear relationship is y = 3x + 2 ⇒ B

Step-by-step explanation:

<em>To solve the question substitute the x in the equation by the x-coordinate of each point to find y, if y equals the y-coordinate of the point, then the point is on the graph of the equation</em>

A.

∵ y = 2x + 3

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 2(0) + 3

∴ y = 0 + 3 = 3

∵ The y-coordinate is 2

∴ The point (0, 2) does not lie on the graph of the relationship

∴ The equation y = 2x + 3 doesn't represent the equation of the relationship

B.

∵ y = 3x + 2

→ Use the first point (0, 2)

∵ x = 0

→ Substitute x by 0 in the equation

∴ y = 3(0) + 2

∴ y = 0 + 2 = 2

∵ The y-coordinate is 2

∴ The point (0, 2) lies on the graph of the relationship

→ Use the second point (1, 5)

∵ x = 1

→ Substitute x by 1 in the equation

∴ y = 3(1) + 2

∴ y = 3 + 2 = 5

∵ The y-coordinate is 5

∴ The point (1, 5) lies on the graph of the relationship

→ Use the third point (3, 11)

∵ x = 3

→ Substitute x by 3 in the equation

∴ y = 3(3) + 2

∴ y = 9 + 2 = 11

∵ The y-coordinate is 11

∴ The point (3, 11) lies on the graph of the relationship

→ Use the fourth point (2, 7)

∵ x = 2

→ Substitute x by 2 in the equation

∴ y = 3(2) + 2

∴ y = 6 + 2 = 8

∵ The y-coordinate is 7

∴ The point (2, 7) doesn't lie on the graph of the relationship

∴ The equation of the linear relationship is y = 3x + 2

3 0
2 years ago
If ΔABC and ΔGEF are congruent by the ASA criterion, which pair of angles must be congruent?
suter [353]

Answer:


Step-by-step explanation:

If we take the below diagram for the given triangles, then ∠B=∠E and ∠A=∠G if AB=GE or if BC=EF, then corresponding angles will be equal.

Therefore, if we rotate the diagram, then also the angles will remain the same.

7 0
3 years ago
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Two actors who are pretending to be ninjas are flying toward each other with the help of wires. pretend ninja number one is flyi
Kryger [21]

Answer:

It'll take them 7.334 s to collide.

Step-by-step explanation:

Since the two ninjas are moving towards each other their relative speed is the sum of each individual speed, therefore:

v = 10 + 12 = 22 \text{ ft/s}

Since they are a 88 feet apart, then we can calculate the time it'll take them to hit each other is:

\Delta S =  v*t

t = \frac{\Delta S}{v}

Applying the data from the problem, we have:

t = \frac{88}{12} = 7.334 \text{ s}

It'll take them 7.334 s to collide.

7 0
3 years ago
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