Hello!
The formula for the slope of a line given two points is [tex] \frac{ y_{2}- y_{1} }{ x_{2}- x_{1} } [/tex], where the ones and twos just represent x or y values from a certain point on the line. Basically, it is [tex] \frac{rise}{run} [/tex].
Statement A does not have similar numbers next to it. It must be the same two numbers (1, 2, 0, etc.) next to it in order for the slope to be calculated correctly. This equation shows that there are probably about four different points we are given, and that is not how we calculate the slope.
Statement B says that [tex] \frac{run}{rise} [/tex] is the slope. This is incorrect. This is the opposite of the slope equation. We want [tex] \frac{rise}{run} [/tex], or [tex] \frac{y}{x} [/tex], so this statement is not true.
Statement C has two ordered pair numbers (0 and 1), where 0 represents the numbers in one ordered pair and 1 represents the values in the other. It is basically the same thing as the ones and twos in the initial slope equation, just represented by different numbers. Statement C is true in terms of the slope of the line.
Statement D says that the slope is [tex] \frac{rise}{run} [/tex]. As we have said before, this is correct in terms of the slope of a line. Statement D is correct.
Statement E has matching numbers, but we are not given full ordered pairs. We are only given one value from an ordered pair, and the top and bottom of this equation is the same, therefore our slope would be one no matter what numbers we plugged in, so therefore it is incorrect.
Statement F adds at the bottom.This happens when subtracting negative numbers but then again your initial instruction was to subtract not to add. Therefore this statement is not true.
The correct statements are Statement C and Statement D.
I hope this helps!
