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

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.

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