Question

Write the equation of a line in Slope Intercept Form that passes through (−2,5) and (3,15).

Answer 1

`\displaystyle y = 2x + 9`

Explanation:

First, find the rate of change [slope]:

`\displaystyle (-y_1 + y_2)/(-x_1 + x_2) = m \\ \\ (-5 + 15)/(2 + 3) = (10)/(5) = 2`

Then, plug the coordinates into the Slope-Intercept Formula instead of the Point-Slope Formula because since you get it done much faster that way. It does not matter which ordered pair you choose:

15 = 2[3] + b

6

`\displaystyle 9 = b \\ \\ y = 2x + 9`

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5 = 2[−2] + b

−4

`\displaystyle 9 = b \\ \\ y = 2x + 9`

** You see? I told you it did not matter which ordered pair you choose because you will always get the exact same result.

I am joyous to assist you anytime.