Question : Find the coordinates of the points where the graph $57x – 19y = 399$ cuts the coordinate axes.
Option 1: x-axis at(–7, 0) and y-axis at (0, –21)
Option 2: x-axis at(–7, 0) and y-axis at (0, 21)
Option 3: x-axis at (7, 0) and y-axis at (0, –21)
Option 4: x-axis at (7, 0) and y-axis at (0, 21)
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Correct Answer: x-axis at (7, 0) and y-axis at (0, –21)
Solution : $57x-19y=399$ ⇒ $\frac{57x}{399}-\frac{19y}{399} = 1$ ⇒ $\frac{x}{7}-\frac{y}{21} = 1$ -------------(i) Comparing it with the equation of a line: $\frac{x}{a}+\frac{y}{b} = 1$ x-intercept = $a$ = 7 y-intercept = $b$ = –21 The line, $57x-19y=399$, cuts the x-axis at (7, 0) and the y-axis at (0, –21) Hence, the correct answer is 'x-axis at (7, 0) and y-axis at (0, –21)'.
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