If (12m, m) and (18m, 6m) are two points on the graph of a line, and m is not equal to zero, what is the slope of the line? Choices: F. -5/6m G. 6/5 H. 5/6
Mathematics · Middle School · Thu Feb 04 2021
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To find the slope of the line, we can use the formula for the slope (m) which is given by the change in y-coordinates divided by the change in x-coordinates:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Given two points (12m, m) and (18m, 6m), we can plug these into the formula. Let's call (12m, m) as (x_1, y_1) and (18m, 6m) as (x_2, y_2):
\[ m = \frac{6m - m}{18m - 12m} \]
Now we simplify the equation:
\[ m = \frac{5m}{6m} \]
Since m is not equal to zero, we can divide both numerator and denominator by m to get the slope:
\[ m = \frac{5}{6} \]
The slope of the line is therefore 5/6, and the correct choice is H. 5/6.