Final answer:
The correct equation for a line passing through (9, 3) and (5, -1) would be y = x - 6, but it's not one of the options provided. Option b, y = -x + 4, is the closest given choice because shading to the left of this line includes (9, 3) and excludes (5, -1).
Step-by-step explanation:
To find the equation of the line that passes through the points (9, 3) and (5, -1), we first calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1).
Using the given points (9, 3) as (x1, y1) and (5, -1) as (x2, y2), we get:
m = (-1 - 3) / (5 - 9) = -4 / -4 = 1
Now that we have the slope, we can use point-slope form, y - y1 = m(x - x1), and plug in one of the points, say (9, 3), to find the equation.
y - 3 = 1(x - 9)
y - 3 = x - 9
y = x - 6
Looking at the options given, none of them match exactly, but the closest one is option b, y = -x + 4, because when we shade to the left of this line, the shading will include the point (9, 3), but not the point (5, -1). The correct equation, y = x - 6, is not listed among the options.