Gb) Graph the relation : \( x-4 y=4 \) and if the straight line representing the relation intersects the \( X \)-axis at the point \( A \) and the \( y \)-axis at the point \( B \), find the area of the triangle \( O A B \) where \( O \) is the origin point.
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To graph the relation \( x - 4y = 4 \), you can rewrite it in slope-intercept form \( y = \frac{1}{4}x - 1 \). This line intersects the \( X \)-axis when \( y = 0 \), so by substituting, we find \( A(8, 0) \). To find the intersection with the \( y \)-axis, set \( x = 0 \): \( B(0, -1) \). The area of triangle \( OAB \) is calculated using the formula for the area of a triangle, \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \). Here, the base \( OA \) is 8 units and the height \( OB \) is 1 unit. Thus, the area is \( \frac{1}{2} \times 8 \times 1 = 4 \) square units.