Final answer:
To derive the equation of a line perpendicular to y = -4/3x - 1 and passing through (3, 4), we determine the negative reciprocal of the original slope (-4/3), which is 3/4, and use the point-slope form. The resulting equation is y = 3/4x + 13/4.
Step-by-step explanation:
To find the equation of a line that is perpendicular to another line, we need to determine the slope of the original line. The provided equation of the line is y = -4/3x - 1. Lines that are perpendicular to each other have slopes that are negative reciprocals. So, the slope of the perpendicular line would be the negative reciprocal of -4/3, which is 3/4.
Now that we have the slope of the perpendicular line, we will use the point-slope form to find the equation of the line that passes through the coordinate (3, 4). The point-slope form is y - y1 = m(x - x1), where m is the slope, and (x1, y1) is the given point. Plugging the values in gives us y - 4 = 3/4(x - 3).
To express this equation in slope-intercept form (y = mx + b), we distribute 3/4 to both x - 3 and then add 4 to both sides, leading to:
y = 3/4x + 13/4