which equation has the least steep graph?y=1/2x+2 or y=10x-8 or y=4x-3 or y=-3/4x+5?

Question

steepness of graph

Answer 1

To determine the "steepness" of a graph, you need to look at the absolute value of slope of the graph. All these equations are in slope-intercept form, y=mx+b, where m is the slope. So the slopes we have are 1/2, 10, 4, and -3/4. The absolute values of these slopes are 1/2, 10, 4, and 3/4. The greater the value of the slope, the "steeper" the slope is, and vice versa. So the smallest value of the absolute value of these slopes is 1/2. So the equation with the least steep graph would be y=1/2x+2. You can confirm this by graphing all four equations.

Answer 2

The coefficient by "x" (the slope) in slope-intercept form of linear equation (y=mx+b) indicate how fast the graph is going up (if slope is positive) or down (if slope is negative). The bigger absolute value of the number - the steeper the graph.
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y = (1/2)x + 2 has the least steep graph
y =     10x - 8 has the greatest steep graph
y =       4x - 3
y = (-3/4)x + 5