Question

11 The table below shows pairs of values that satisfy a linear function.2 -53 64 175 286 397 50What is the y-intercept of the graph of this function?

Answer 1

10)

we get the points from the table are (2,12) and (8,0).

Consider the line equation.

`y=mx+b`

where b is the y=intercept.

Substitute x=2 and y=12, we get

`12=m(2)+b`

`12=2m+b`

`12-b=2m`

`(12-b)/(2)=m`

Substitute x=8 and y=0 in the line equation, we get

`0=8m+b`

Substitute m value in this equation to find the value of b.

`0=8((12-b)/(2))+b`

`0=4(12-b)+b`

`0=4*12-4b+b`

`0=48-3b`

`3b=48`

Dividing both sides by 3, we get

`b=(48)/(3)=16`

Hence the y-intercept is 16.

11)

we get the points from the table are (2,-5) and (4,17).

Consider the liner function.

`y=mx+b`

where b is the y-intercept.

Substitute x=2 and y=-5, we get

`-5=2m+b`

`-5-b=2m`

`(-5-b)/(2)=m`

`m=(-5-b)/(2)`

Substitute x=4 and y=17 in the equation, we get

`17=4m+b`

Substitute the value of m in this equation to find the value of b.

`17=4((-5-b)/(2))+b`

`17=2(-5-b)+b`

`17=-10-2b+b`

`17+10=-b`
`b=-27`

Hence the y-intercept is -27.