Final answer:
To find an equation of a line that is perpendicular to y = 5x + 3 and passes through (2, 4), use the point-slope form of a line.
Step-by-step explanation:
To find an equation of a line that is perpendicular to y = 5x + 3 and passes through the point (2, 4), we need to determine the slope of the given line and then find the negative reciprocal to obtain the slope of the perpendicular line.
The given equation is in the form y = mx + b, where m is the slope. In this case, the slope of y = 5x + 3 is 5.
The negative reciprocal of 5 is -1/5, so the slope of the perpendicular line is -1/5. Using the point-slope form of an equation, we can substitute the slope (-1/5) and the coordinates of the point (2, 4) into the equation y - y1 = m(x - x1).
Simplifying the equation gives us y - 4 = -1/5(x - 2). Multiplying through by -5 and rearranging the equation in slope-intercept form y = mx + b, we have y = -1/5x + 6.