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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