10)
we get the points from the table are (2,12) and (8,0).
Consider the line equation.
[tex]y=mx+b[/tex]
where b is the y=intercept.
Substitute x=2 and y=12, we get
[tex]12=m(2)+b[/tex]
[tex]12=2m+b[/tex]
[tex]12-b=2m[/tex]
[tex]\frac{12-b}{2}=m[/tex]
Substitute x=8 and y=0 in the line equation, we get
[tex]0=8m+b[/tex]
Substitute m value in this equation to find the value of b.
[tex]0=8(\frac{12-b}{2})+b[/tex]
[tex]0=4(12-b)+b[/tex]
[tex]0=4\times12-4b+b[/tex]
[tex]0=48-3b[/tex]
[tex]3b=48[/tex]
Dividing both sides by 3, we get
[tex]b=\frac{48}{3}=16[/tex]
Hence the y-intercept is 16.
11)
we get the points from the table are (2,-5) and (4,17).
Consider the liner function.
[tex]y=mx+b[/tex]
where b is the y-intercept.
Substitute x=2 and y=-5, we get
[tex]-5=2m+b[/tex]
[tex]-5-b=2m[/tex]
[tex]\frac{-5-b}{2}=m[/tex]
[tex]m=\frac{-5-b}{2}[/tex]
Substitute x=4 and y=17 in the equation, we get
[tex]17=4m+b[/tex]
Substitute the value of m in this equation to find the value of b.
[tex]17=4(\frac{-5-b}{2})+b[/tex]
[tex]17=2(-5-b)+b[/tex]
[tex]17=-10-2b+b[/tex]
[tex]17+10=-b[/tex][tex]b=-27[/tex]
Hence the y-intercept is -27.
