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Answer:
[tex]x - 2y = -10[/tex]
Step-by-step explanation:
1) Use the point-slope formula [tex]y-y_1 = m(x-x_1)[/tex] to write the equation of the line in point-slope form with the given information. From there, we can convert it to standard form. Substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] in the formula.
Since [tex]m[/tex], or the slope, is equal to [tex]\frac{1}{2}[/tex], substitute [tex]\frac{1}{2}[/tex] for [tex]m[/tex] in the formula. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (6,8) into the formula as well. This gives the following equation:
[tex]y-8 = \frac{1}{2} (x-6)[/tex]
2) Now, convert the equation above into standard form, represented by the equation [tex]Ax + Bx = C[/tex]. Expand the right side, move the terms with the variables to the left side, then move the constants to the right side. Make sure that [tex]A[/tex] isn't negative and all the terms are integers and relatively prime.
[tex]y-8=\frac{1}{2}(x-6)\\y-8 = \frac{1}{2} x-3\\-\frac{1}{2} x+y -8=-3\\-\frac{1}{2} x+y=5\\x -2y = -10[/tex]
So, the answer is [tex]x - 2y = -10[/tex].