Final answer:
To find the equation of a line perpendicular to y = -1/5x - 1 that passes through (1, 3), we determine the slope to be 5 and use the point-slope form to get the equation y = 5x - 2.
Step-by-step explanation:
The equation we are examining is y = -1/5x - 1; we need to find an equation that is perpendicular to this and goes through the point (1, 3). First, recall that if two lines are perpendicular, the slopes are negative reciprocals of each other. The slope of our given equation is -1/5, so the slope of the line that is perpendicular to this must be 5 because -1/5 * 5 = -1. With this new slope, we can use the point-slope form of a linear equation, y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line goes through. In this case, x1 is 1 and y1 is 3. Plugging in the values, we get y - 3 = 5(x - 1). Solving for y, we simplify to get the equation y = 5x - 2 which is in slope-intercept form y = mx + b. This is the equation of the line that is perpendicular to the given line and passes through the point (1, 3).