Final answer:
To find an equation that is perpendicular to the line y=5x+3 and passes through (2,4), use the fact that perpendicular lines have slopes that are negative reciprocals of each other. The equation of the line perpendicular to y=5x+3 and passing through (2,4) is y = -1/5x + 24/5.
Step-by-step explanation:
To find an equation that is perpendicular to the line y=5x+3 and passes through (2,4), we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other. The slope of the given line is 5, so the slope of the perpendicular line will be -1/5.
Using the slope-intercept form of a line, y=mx+b, where m is the slope and b is the y-intercept, we can substitute the given point (2,4) and the slope -1/5 into the equation to solve for b: 4 = (-1/5)(2) + b. Solving for b, we get b = 4 + 2/5 = 24/5.
Therefore, the equation of the line perpendicular to y=5x+3 and passing through (2,4) is y = -1/5x + 24/5.