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How do i write these in slope-intercept form? (show work)
1) 13x - 11y = -12
2) through (1, 2) ; m = 7
3) through (3, -1) ; m = -1
4) through (-2, 5) ; m = -4
5) through (3, 5) ; m = 5/3 (< fraction)

Verified Answer :

\(The\ slope-intercept\ form:y=mx+b\\\\1)\ 13x-11y=-12\ \ \ \ |subtract\ 13x\ from\ both\ sides\\\\-11y=-13x-12\ \ \ \ \ \ |divide\ both\ sides\ by\ (-11)\\\\\boxed{y=\frac{13}{11}x+\frac{12}{11}}\)


\(2)\ m=7\to y=7x+b\\\\the\ point:(1;\ 2)\to substitute\ x=1\ and\ y=2\ to\ equation:\\\\7(1)+b=2\\7+b=2\ \ \ \ \ |subtract\ 7\ from\ both\ sides\\b=-5\\\boxed{y=7x-5}\)


\(3)\ m=-1\to y=-x+b\\\\(3;-1)\\\downarrow\\-3+b=-1\ \ \ \ |add\ 3\ to\ both\ sides\\b=2\\\\\boxed{y=-x+2}\)


\(4)\ m=-4\to y=-4x+b\\\\(-2;\ 5)\\\downarrow\\-4(-2)+b=5\\8+b=5\ \ \ \ \ |subtract\ 8\ from\ both\ sides\\b=-3\\\\\boxed{y=-4x-3}\)


\(5)\ m=\frac{5}{3}\to y=\frac{5}{3}x+b\\\\(3;\ 5)\\\downarrow\\\frac{5}{3}(3)+b=5\\5+b=5\ \ \ \ |subtract\ 5\ from\ both\ sides\\b=0\\\\\boxed{y=\frac{5}{3}x}\)

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