Final answer:
The equation of the line that is perpendicular to y = -4/3x - 3 and passes through the point (4, 5) is y = 3/4x + 2. This is found by taking the negative reciprocal of the original line's slope to get the perpendicular slope and then using the point-slope form to find the specific equation.
Step-by-step explanation:
The student has asked how to find the equation of a line that is perpendicular to the given line y = -4/3x - 3 and that passes through the point (4, 5). To do this, we need to find the slope of the line that is perpendicular to the given line.
Since the slope of the given line is -4/3, the slope of the perpendicular line will be the negative reciprocal, which is 3/4. We then use this slope and the point (4, 5) to write the equation of the perpendicular line using the point-slope form, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point. The equation will then be simplified to the slope-intercept form, y = mx + b, to find the y-intercept b.
To find b, we substitute x with 4 and y with 5 into the equation y - 5 = 3/4(x - 4) and solve for b. Carrying out the calculations, we get b = 2. Upon substitution, the final equation of the line is y = 3/4x + 2.