Question

write the equation of the line that passes through the points (3, 6) and (5, 18) using function notation. a. f(x) = 2x 12 b.f(x) = 6x − 12 c. y = 2x 12 d.y = 6x − 12

Answer 1

The slope-intercept form:
`y= mx + b`

The slope-point form:
`y-y_1=m(x-x_1)`

The slope:
`m=(y_2-y_1)/(x_2-x_1)`


`(3; 6)\to x_1=3;\ y_1=6\\(5;\ 18)\to x_2=5;\ y_2=18`

subtitute


`m=(18-6)/(5-3)=(12)/(2)=6`


`y-6=6(x-3)\\\\y-6=6x-18\ \ \ \ |add\ 6\ to\ both\ sides\\\\y=6x-12`

Answer: b. f(x)=6x - 12