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

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