Given a linear equation y = mx + b, we refer to the coefficient 'm' as the slope. The greater the magnitude of 'm', the steeper the slope.
i.e. y = 4x has a steeper slope than y = 1.5x, but has just as steep a slope as y = -4x
In the options provided, we need to find the slope of each
For I. the points (-3, 16), (0, 1), and (4, -19) fall on the same line. We can find the slope by calculating (y2-y1)/(x2-x1) for any two points.
(16-1)/(-3-0) = 15/-3 = -5
or (-19-1)/(4-0) = -20/4 = -5
Our slope, 'm', has a value of -5
For II.
-2x - y = 10
add 'y' to both sides and subtract 10 from both sides to get 'y = mx + b'
y = -2x + 10
Now we see 'm' = -2
For III.
Pick two points on the graph and find 'm' by solving (y2-y1)/(x2-x1)
i.e. (0, 4) and (5, 0)
m = (4-0)/(0-5) = -4/5 = -0.8
Of the three lines I, II, and III, the slopes have steepnesses with magnitudes of 5, 2, and 0.8 respectively. Therefore I has the steepest slope.
