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Easy

Question

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

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) = (y2-y1) × (x-x1)

(x2-x1)

## 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).

### 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

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