Answer:
Option C
Step-by-step explanation:
In the slope-intercept form of linear equation
[tex]y = m*x + b [tex]
"m" indicates the slope (meaning how fast y varies with respect to x)
"b" indicates the y-intercept of the line (at point (0,b))
In this exercise, we are asked for the fastest variation of y with respect to x.
In other words, the bigger absolute value of the slope, the steeper the graph.
Notice that, taking absolute value, we cover both cases when the line is incresing (positive slope) and when the line is decreasing (negative slop)
Let's do the calculations...
[tex]
y = 4x - 3 => |slope| = |4| = 4
y = (-3/4)x + 5 => |slope| = |-3/4| = 3/4 = 0.75
y = (1/2)x + 2 => |slope| = |1/2| = 1/2 = 0.5 (least steep)
y = 10x - 8 => |slope| = |10| = 10
Comparing the values, we conclude that y = (1/2)x + 2 has the least steep graph
[/tex]
