Question

What equation in slope intercept form represents the line that passes through the two points (5,8) (7,3)

Answer 1

`\displaystyle y = -2(1)/(2)x + 20(1)/(2)`

Explanation:

First, find the rate of change [slope]:

`\displaystyle (-y_1 + y_2)/(-x_1 + x_2) = m \\ \\ (-8 + 3)/(-5 + 7) = -(5)/(2) = -2(1)/(2)`

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

3 = −2½[7] + b

−17½

`\displaystyle 20(1)/(2) = b \\ \\ y = -2(1)/(2)x + 20(1)/(2)`

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8 = −2½[5] + b

−12½

`\displaystyle 20(1)/(2) = b \\ \\ y = -2(1)/(2)x + 20(1)/(2)`

** 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.