Final answer:
To find the equation of the line through (-8, 8) perpendicular to Y = -5/6x + 4, we need to find the slope of the perpendicular line and use the point-slope form of a linear equation. The equation in slope-intercept form is y = 6/5x - 32/5.
Step-by-step explanation:
First, let's find the slope of the given line. The equation of the line is Y = -5/6x + 4, so the slope is -5/6. Since we're looking for a line perpendicular to this one, the slope of the perpendicular line will be the negative reciprocal. Therefore, the slope of the perpendicular line is 6/5.
Next, we can use the point-slope form of a linear equation to find the equation of the perpendicular line. We'll use the point (-8, 8) and the slope 6/5. The equation is y - y1 = m(x - x1).
Plugging in the values, we get y - 8 = (6/5)(x - (-8)). Simplifying, we get y - 8 = (6/5)(x + 8).
Finally, let's rewrite the equation in slope-intercept form, which is y = mx + b. By distributing the (6/5) to the terms inside the parentheses and rearranging the equation, we have y = 6/5x + 48/5 - 8. Simplifying further, we get y = 6/5x - 32/5.
Therefore, the equation in slope-intercept form of the line through (-8, 8) perpendicular to Y = -5/6x + 4 is y = 6/5x - 32/5.