What is equation of line AB if A(-1,1)B(3,7)?

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There exists more formulas available to write the equation of a line. You need to select one formula depending on information provided by the problem, such that:

`(AB): y - y_A = (y_B - y_A)/(x_B - x_A)(x - x_A)`

Replacing the corresponding values of coordinates in equation yields:

`(AB): y - 1 = (7 - 1)/(3 - (-1))(x - (-1))`

`(AB): y - 1 = (6/4)(x + 1)`

`(AB): y - 1 = (3/2)(x + 1) => (AB): 2y - 2 = 3x + 3`

`(AB): 3x - 2y + 3 + 2 = 0 => (AB): 3x - 2y + 5 = 0`

**Hence, evaluating the equation of the line (AB), under the given conditions, yields **` (AB): 3x - 2y + 5 = 0.`

Another approach to use to find the equation is as follows:

Step 1: Find the slope: m = 7 - (1)/ 3-(-1)

m = 3/2

Step 2: Substitute slope and *either* of the given points into the slope-intercept form. We'll use the point (3,7). Solve for "b" which is the y intercept.

y = mx + b

7 = 3/2(3) + b

7 = 9/2 + b

5/2 = b

Step 3: Substitute the slope which is 3/2 and the y intercept which is 5/2 into the slope intercept form.

**Answer: y = 3/2x + 5/2**

Slope intercept form makes the equation easy to graph!

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