Final answer:
The equation in slope-intercept form is y + 5 = (-3/4)(x - 4).
Step-by-step explanation:
To find the equation of a line parallel to the line 3x+4y=8 that passes through the point (4,-5), we first need to determine the slope of the given line.
To do this, we can rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Starting with the original equation, 3x+4y=8, we can isolate y by subtracting 3x from both sides, giving us 4y = -3x + 8.
Next, we divide both sides by 4 to solve for y, resulting in y = (-3/4)x + 2.
Since parallel lines have the same slope, the line parallel to 3x+4y=8 will also have a slope of -3/4.
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), we can substitute the given point (4,-5) and the slope -3/4 into the equation and simplify to find the final equation of the parallel line: y + 5 = (-3/4)(x - 4).