The line \( 8 x-4 y=7 \) correctly written in slope-intercept form is a.) \( y=2 x=\frac{7}{4} \) b.) \( y=-2 x+\frac{7}{4} \) c.) \( y=-\frac{4}{8} x+\frac{7}{8} \) d.) \( y=\frac{1}{2} x-\frac{7}{8} \)
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Beyond the Answer
To write the line \( 8x - 4y = 7 \) in slope-intercept form \( y = mx + b \), we need to solve for \( y \). Rearranging the equation gives us: \[ -4y = -8x + 7 \] Dividing everything by -4: \[ y = 2x - \frac{7}{4} \] This means the correct answer is not listed among the options, but if we were to choose the closest representation based on a potential miscalculation, the correct slope-intercept form simplifies to \( y = 2x - \frac{7}{4} \). Now for some bonus insights! 🌟 When transforming an equation into slope-intercept form, it's always a good approach to isolate \( y \) first! Remember, the slope (m) represents how steep the line is, while the y-intercept (b) indicates where the line crosses the y-axis. This can help visualize graphed lines and their behaviors! Struggling with negative signs? A common mistake occurs when distributing negatives. Always check your work step-by-step. If you mess up a single negative, it can cost you the correct direction of your slope! Just take a moment to verify your arithmetic—it's worth it!