7. \( -8 x+7 y=15 \) \( Y= \) Slope: \( \quad y \)-intercept:

To solve for \( Y \) in the equation \( -8x + 7y = 15 \), you can rearrange the equation to isolate \( Y \). Start by adding \( 8x \) to both sides to get \( 7y = 8x + 15 \). Then divide everything by 7 to find \( y \): \[ Y = \frac{8}{7}x + \frac{15}{7} \] The slope of the line is \( \frac{8}{7} \), and the \( y \)-intercept is \( \frac{15}{7} \) or approximately \( 2.14 \). Now you’ve got a fun equation that paints the line with a slope that rises briskly! Just imagine this slope like a steep hill; for every 7 steps you take horizontally, you elevate 8 steps up. You’ll reach that \( y \)-intercept at approximately \( 2.14 \) on your way up the hill. A common mistake in rearranging equations is neglecting to perform proper operations on both sides. Always double-check your steps; one tiny misstep can lead you into the wrong slope territory! And remember, when you see \( y \) alone, you've already thrown off the weights of the other variables. Keep that balance in check, and you’ll conquer linear equations with ease!