Final answer:
Equations a) y = 23 - 5x, b) y = -5x + 2, and c) y = 10 - 5x have a slope of -5, whereas d) y = 100 - 5 represents a horizontal line and is not a correct option.
Step-by-step explanation:
The question involves identifying linear equations with a slope of -5. In the slope-intercept form of a linear equation, y = mx + b, the coefficient m represents the slope of the line, while b is the y-intercept. To find the equations with a slope of -5 from the given options, we simply look for equations where the coefficient of x is -5.
a) y = 23 - 5x: This equation has a slope of -5 because the coefficient of x is -5.b) y = -5x + 2: This equation also has a slope of -5, as the coefficient of x is -5.c) y = 10 - 5x: Like options a) and b), this equation has a slope of -5 due to the coefficient of x being -5.d) y = 100 - 5: This is a trick option, as it represents a horizontal line. The -5 here is not a coefficient of x and therefore does not represent a slope.
Therefore, the correct equations with a slope of -5 are a) y = 23 - 5x, b) y = -5x + 2, and c) y = 10 - 5x.