Question

The graph of a function is a line that passes through the coordinates (2, 11) and (8, 14).Part AWhich shows how to find the rate of change for the function?A.
`(8 - 2)/(14 - 11)`B.
`(14 - 11)/(8 - 2)`C.
`(14 - 8)/(11 - 2)`D.
`(11 - 2)/(14 - 8)`Part BWhich is an equation in terms of x and y for this function?A.
`y = (1)/(2) x + 10`B.
`y = (2)/(3) x + 9`C.
`y = (3)/(2) x + 8`D.
`y = 2x + 7`

Answer 1

The slope of a line is defined as rise/run. In other words, it is the change in the y-coordinate over the change in x-coordinate.

Now, for the points (2, 11) and (8, 14) the change in y-coordinate is

`14-11`

and the change in the x-coordinate is

`8-2`

Therefore, the slope is

`(14-11)/(8-2)`

which is choice B.

Part B.

The equation of a line is of the form

`y=mx+b`

where m is the slope and b is the y-intercept.

Now, the slope we found from part A is

`m=(14-11)/(8-2)=(3)/(6)=(1)/(2)`

Therefore,

`y=(1)/(2)x+b`

we now just need to find b.

We find the y-intercept b using the point (2. 11) and putting in y =11 and x = 2 in the above equation gives

`11=(1)/(2)(2)+b`
`11=1+b`
`\therefore b=10`

Hence, the equation of the line is

`y=(1)/(2)x+10`

which is choice A,