Answer:
[tex]\displaystyle 3x - 2y = 13\:or\:y = 1\frac{1}{2}x - 6\frac{1}{2} \\ [0, -6\frac{1}{2}] \\ 1\frac{1}{2} = m[/tex]
Step-by-step explanation:
First, figure the rate of change [slope] out:
[tex]\displaystyle \frac{-y_1 + y_2}{-x_1 + x_2} = m \\ \\ \frac{-1 + 16}{-5 + 15} = \frac{15}{10} = 1\frac{1}{2} \\ \boxed{1\frac{1}{2} = m}[/tex]
Now locate the initial value [y-intercept] by plugging an ordered pair into the slope-intercept formula. It does not matter which ordered pair you use:
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[tex]\displaystyle y = mx + b[/tex]
16 = 1½[15] + b >> [tex]\displaystyle 16 = 22\frac{1}{2} + b; -6\frac{1}{2} = b[/tex]
OR
1 = 1½[5] + b >> [tex]\displaystyle 1 = 7\frac{1}{2} + b; -6\frac{1}{2} = b[/tex]
[tex]\displaystyle [0, -6\frac{1}{2}][/tex]
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You now have your initial value. All that is left is to write the equation of this line, which can be written two ways:
> Slope-Intercept Form
[tex]\displaystyle y = 1\frac{1}{2}x - 6\frac{1}{2}[/tex]
> Standard Form [tex]\displaystyle [Ax + By = C][/tex]
y = 1½x - 6½
- 1½x - 1½x
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–1½x + y = –6½ [We CANNOT leave the equation this way, so multiply by –2 to eradicate the fraction\denominatour (if you wrote the equation as mixed numbers\if you wrote the equation as improper fractions).]
–2[–1½x + y = –6½]
[tex]\displaystyle 3x - 2y = 13[/tex]
With that, you have defined all the information.
[tex]\displaystyle -3x + 2y = -13[/tex]
*About this equation, INSTEAD of multiplying by –2, you multiply by its oppocite, 2. Now, you can leave it like this, but UNIVERSALLY, the A-term is positive, so you must multiply the negative out as well.
I am joyous to assist you at any time.
