Final answer:
To find an equation parallel to y = -2/3x + 6 that goes through the point (5,-4), use the point-slope form of a linear equation and plug in the coordinates of the point and the slope.
Step-by-step explanation:
To find an equation parallel to y = -2/3x + 6 that passes through the point (5,-4), we need to use the fact that parallel lines have the same slope. The given equation is in slope-intercept form, where the coefficient of x (-2/3) represents the slope.
So, the slope of the parallel line will also be -2/3. Plugging in the coordinates of the point (5,-4) and the slope (-2/3) into the point-slope form of a linear equation, we get: y - y1 = m(x - x1)
where x1 = 5, y1 = -4, and m = -2/3. Simplifying this equation will give us the equation parallel to y = -2/3x + 6 that goes through the point (5,-4).