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Use points (2,5) and (4,8) find slope intercept and standard form

User Kevek
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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.

====

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).

Use points (2,5) and (4,8) find slope intercept and standard form-example-1
User Maki
by
8.8k points

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