Maths-
General
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

hintHint:

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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