Question : What is the equation of the line whose y-intercept is $-\frac{3}{4}$ and making an angle of $45^{\circ}$ with the positive x-axis?
Option 1: $4x–4y=3$
Option 2: $4x-4y=–3$
Option 3: $3x–3y=4$
Option 4: $3x–3y=–4$
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Correct Answer: $4x–4y=3$
Solution : Given: $\theta = 45^{\circ}$, we have $m$ = $\tan45^{\circ}$= 1 The $y$-intercept is given as $-\frac{3}{4}$. Putting the values into the equation, we get: $y = x–\frac{3}{4}$ Or, $4y = 4x–3$ $\therefore$ $4x–4y = 3$ Hence, the correct answer is $4x–4y = 3$.
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