Final answer:
To find the slope-intercept form of a line with slope -1/5 passing through the point (5, -3), we use y = mx + b to calculate the y-intercept b by substituting in the given point, resulting in b = -2. The correct equation should be y = -1/5x - 2; however, this does not match any provided options, suggesting there might be an error.
Step-by-step explanation:
The student is looking to find the slope-intercept form of the equation of a line with a given slope (m) that also passes through a specific point. Given the slope m = -1/5 and the point (5, -3), we can plug these into the slope-intercept form of a line equation, which is y = mx + b, where m is the slope and b is the y-intercept. To find b, we substitute the slope and the coordinates of the point into the equation:
y = (-1/5)x + b
-3 = (-1/5)(5) + b
-3 = -1 + b
b = -3 + 1
b = -2
Thus, the equation of the line is y = -1/5x - 2. However, this option does not appear among the choices provided. We are probably expected to select the closest match, so it seems there is either a typo in the question or the provided options. The provided options have the correct slope but different intercepts. Since we calculated b = -2 and the closest available option that reflects the correct slope is y = -1/5x + 4, it may be likely that there has been a mistake in the options given or in the calculation.