Answer :
[tex]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}}[/tex]
[tex]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}[/tex]
[tex]3)\ m=-1\to y=-x+b\\\\(3;-1)\\\downarrow\\-3+b=-1\ \ \ \ |add\ 3\ to\ both\ sides\\b=2\\\\\boxed{y=-x+2}[/tex]
[tex]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}[/tex]
[tex]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}[/tex]
[tex]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}[/tex]
[tex]3)\ m=-1\to y=-x+b\\\\(3;-1)\\\downarrow\\-3+b=-1\ \ \ \ |add\ 3\ to\ both\ sides\\b=2\\\\\boxed{y=-x+2}[/tex]
[tex]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}[/tex]
[tex]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}[/tex]
Answers have been attached below... Enjoy...
Open up the attachment in a new window to see it in full.
Open up the attachment in a new window to see it in full.
