Answer:
See the attached graph.
Explanation:
Slope Intercept Form takes the form of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is zero). We can take the two given points and find m, the slope. Slope is the Rise/Run of a line. The amount y changes for a change in x. Going from lowest x to highest:
(2,5) and (4,8)
Rise = 8 - 5 = 3
Run = 4 - 2 = 2
Slope -= Rise/Run or 3/2
The equation takes the form y = (3/2)x + b
To find b, enter one of the two points into the above equation and solve for b:
y = (3/2)x + b
5 = (3/2)*2 + b for (2,5)
5 = 3 + b
b = 2
The slope intercept form for these points is y = (3/2)x + 2.
See the attached graph.
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The standard form appears as Ax + By = C
Lets rearrange the slope intercept form that we found above:
y = (3/2)x + 2
2y - 3x = 4 {multiply both sides by 2 and also subtract 3x]
-3x + 2y = 4 [Rearrange]
The attached graph proves both equations are equivalent, and also go through points (2,5) and (4,8).