graph the equation 3x+6y=12 find the slope of a line containing points (-2,8) and (3,5)what is the slope of a horizontal line is

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

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To find the slope of a line given two points, use the formula `m=(y_2-y_1)/(x_2-x_1)` where `x_i,y_i` are the x and y coordinates of thegiven points. (This is `(Delta Y)/(Delta x)` or `"changeiny"/"changeinx"` , or graphically `"rise"/"run"` ; a horizontal line has zero slope as there is no change in the y value).

Given (-2,8) and (3,5) we have `m=(5-8)/(3-(-2))=(-3)/(5)=-3/5`

Note that if you reverse the order you get the same result: `m=(8-5)/(-2-3)=3/(-5)=-3/5` .

To graph a line you can rewrite in slope-intercept form `y=mx+b` , find the intercepts, or use a table to find two points on the line. Since the equation is in standard form the easiest way is to find the intercepts:

Given `3x+6y=12`

`x=0==>y=2` so (0,2) is on the graph.

`y=0==>x=4` so (4,0) is on the graph.

Plot these points in a coordinate plane and connect with a line.

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