Answer:
[tex]y=-4x+7[/tex]
Step-by-step explanation:
Use the slope-intercept formula: [tex]y=mx+b[/tex] where m is the slope and b the y-intercept.
Find the slope using the slope formula for when you know two points:
[tex](-1,11)(3,-5)\\\\(-1(x1),11(y1))\\(3(x2),-5(y2))\\\\\frac{y(2)-y(1)}{x(2)-x(1)}[/tex]
Insert values:
[tex]\frac{-5-11}{3-(-1)}[/tex]
Simplify parentheses:
[tex]\frac{-5-11}{3+1}[/tex]
Simplify:
[tex]\frac{-16}{4} =-4[/tex]
Insert into equation:
[tex]y=-4x+b[/tex]
Find the y-intercept by taking one of the points and inserting into the equation:
[tex](3,-5)\\(3(x),-5(y))\\-5=-4(3)+b[/tex]
Solve for b
[tex]-5=-4*3+b\\-5=-12+b\\-5+12=-12+12+b\\-5+12=b\\7=b[/tex]
7 is the y-intercept. Insert into the equation:
[tex]y=-4x+7[/tex]
Done.
