Question

# Which of the following lines pass through origin?

- y = x - 1
- x = 2
- y = 1
- y = 5x

Hint:

### A line is said to be passing through a given point when the co-ordinanates of that point satisfies the equation I.e. LHS = RHS.

## The correct answer is: y = 5x

### Step-by-step solution:-

To check whether the given lines pass through origin (0,0) or not, we substitute x = 0 & y = 0 in all of the equations and check whether LHS = RHS or not.

a. y = x – 1

∴ 0 = 0 - 1

∴ 0 ≠ -1

∴ LHS ≠ RHS

b. x = 2

∴ 0 ≠ 2

∴ LHS ≠ RHS

c. y = 1

∴ 0 ≠ 1

∴ LHS ≠ RHS

d. y = 5x

∴ 0 = 5 (0)

∴ 0 = 0

∴ LHS = RHS

Since option d satisfies the required condition i.e. Point (0,0) satisfies the equation of line y = 5x, option d is the correct answer.

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Carrie, a packaging engineer, is designing a container to hold 12 drinking glasses shaped as regular octagonal prisms. Her initial sketch of the top view of the base of the container is shown above.

Carrie redesigned the container because the initial sketch did not account for cushioning material between the glasses. The area of the base of the newly designed container is greater than the area of the base in the initial sketch. What is the area, in square inches, of the base of the newly designed container?

**Note:**

There is a shorter way of doing this problem. There is a simple rule followed while increasing or decreasing a value by a certain percentage. When we decrease a quantity by x%, we multiply the quantity by (1-0.x). Whereas when we increase a quantity by x%, we multiply it with (1+0.x).

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Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.

¶A line's slope can be determined using its two points (x_{1}, y_{1}) and (x_{2}, y_{2}). The formula (y_{2} - y_{1}) / is used to find the change in y and divided by the change in x. (x_{2} - x_{1}).

### Find the equation of line that passes through the point (2, -9) and which is perpendicular to the line x = 5.

Use the perpendicular line formula to determine whether two given lines are perpendicular. For example, when the slope of two lines is given to compare, we can use the perpendicular line's formula. A 90-degree angle is created by two lines that are perpendicular to one another.

Slope exists on every line. Because it shows how quickly our line is rising or falling, the slope of a line reveals how steep a line is. Mathematically, the slope of a line is known as the ratio of change in the line's y-value to the change in its x-value.

¶A line's slope can be determined using its two points (x_{1}, y_{1}) and (x_{2}, y_{2}). The formula (y_{2} - y_{1}) / is used to find the change in y and divided by the change in x. (x_{2} - x_{1}).