Question

# A line passes through the points (-6, 4) and (-2,8). Where does the line intersect the X-axis and the Y-axis?

## The correct answer is: Equation of the given line is y = x + 10 and this line intersects the x-axis at (-10,0) and y-axis at (0,10)

### Hint:-

1. X-intercept is the point on a line at which that line intersects the X-axis and at this point, y-coordinate = 0.

2. Y-intercept is the point on a line at which that line intersects the Y-axis and at this point, x-coordinate = 0.

3. A line is said to be passing through a point when the coordinates of such point satisfy equation of the given line.

4. When we have 2 points that lie on a given line then we can find the equation of the said line by using the 2-point formula-

(y-y1) = × (x-x1)

Step-by-step solution:-

The given line passes through the point (-6,4) & (-2,8).

Hence, x1 = -6, y1 = 4, x2 = -2 & y2 = 8

(y-y1) = (y2-y1) * (x-x1)

(x2-x1)

∴ (y-4) = (8-4) * [x- (-6)]

[-2 - (-6)]

∴ y - 4 = 4 * (x + 6)

-2 + 6

∴ y - 4 = 4 * (x + 6)

4

∴ y - 4 = 1 * (x + 6)

∴ y - 4 = x + 6

∴ y = x + 6 + 4

∴ y = x + 10 ............................................ (Equation i)

We need to find the point at which the given line intersects x-axis & y-axis i.e. we need to find the x-intercept and y-intercept of the given line.

X-intercept is the point at which y-coordinate is 0.

∴ we substitute y = 0 in Equation i-

y = x + 10

∴ 0 = x + 10

∴ -10 = x

Y-intercept is the point at which x-coordinate is 0.

∴ we substitute x = 0 in Equation i-

y = x + 10

∴ y = 0 + 10

∴ y = 10

Final Answer:-

∴ Equation of the given line is y = x + 10 and this line intersects the x-axis at (-10,0) and y-axis at (0,10).

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**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).

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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¶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}).

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¶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}).

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**Note:**

A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.

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If the length and width of the container base in the initial sketch were doubled, at most how many more glasses could the new container hold?

**Note:**

A few simple ideas are used in solving this problem, like, area of a rectangle is given by the product of its length and breadth and the basic idea of division.

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Another answer for this problem could be taken as 137 as well.

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### An arc of a circle measures 2.4 radians. To the nearest degree, what is the measure, in degrees, of this arc? (Disregard the degree sign when gridding your answer.)

**Note:**

Another answer for this problem could be taken as 137 as well.

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