Question

Given the slopes of three lines, m1 = 2, m2 = 5. m3 = -4, which line would you say is

Answer 1

The steepest slope is m = 5.

Slope compares the vertical change (the rise) to the horizontal change (the run) when moving from one fixed point to another along the line. To calculate the slope of a line, we use a ratio that compares the change in y (the rise) to the change in x (the run).

Comparing the ratios of the given slopes:

m1 = 2/1
m2 = 5/1
m3 = -4/1

They all have the same change in x (run), but vary in the change in y (rise).

If you envision the slope of m1 as going up 2, and 1 unit to the right, it is not as steep as the slope of m2, which goes up 5 units and 1 unit to the right.

M2 is also steeper than m3, because with m3, you go down only 4 units and 1 unit to the right.

Attached is a screenshot of a graph where it compares the given slopes. As you’ll see from the graph, y = 5x (red line) is the steepest.

Therefore, the correct answer is m = 5.

Answer 2

Compare the slopes of the 4 equations, which is the number in the term with "x".  The slope with highest absolute value is the steepest.  Positive slope means the function is ascending left to right, negative slope means it is descending left to right.  If you only care that it is the steepest, regardless of whether it is ascending or descending, then the answer is (D).