Can you please show me some examples of math problems using a slope of 0, 1/2 or undefined. Please solve problem in dummy terms.   Thank you

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embizze | High School Teacher | (Level 2) Educator Emeritus

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(1) Lines that have slope 0 have graphs that are horizontal lines. The y-values are the same. For example the line y=2. Some points on this line include (-3,2),(-1,2),(0,2),(1,2),`(pi,2)` , etc...

Choose any pair of points from the list to compute the slope -- say (-3,2) and (1,2). Then the slope is `m=(y_2-y_1)/(x_2-x_1)=(2-2)/(1-(-3))=0` .

Note that in slope-intercept form, `y=mx+b` , if the line was y=2 then the slope `m=0`

(2) A line with slope of 1/2 is of the form `y=1/2x+b` where `b` can be any real number. The graph of such a line goes up as you scan from left to right -- for every 2 unitsyou scan to the right, the graph rises by 1 unit.

Example: y=1/2x+3 includes the points (-4,1),(-2,2),(0,3),(1,3.5),(2,4) etc... Note that as x increased 2 units, say from -4 to -2, y increased by 1 unit, here from 1 to 2.

(3) A line with an undefined slope has a graph that is vertical or straight up and down. This is not a function, An example would be x=-2. All of the points have the same x-value, and y can be anything. For this example some points are (-2,-2),(-2,0),(-2,3),(-2,6.135) etc...

When trying to compute the slope, you end up dividing by zero,which is not allowed. Taking the points (-2,-2) and (-2,3) we find the slope: `m=(y_2-y_1)/(x_2-x_1)=(3-(-2))/(-2-(-2))=5/0` which is undefined.

**Note that this graph is an approximation, since this graphing utility, as most, will only graph functions.