Question

Find an equation of the line through these points (15,2.2) (5,1.6). Write answer in a slope-intercept form

Answer 1

`y=(\displaystyle 3)/(\displaystyle 50)x+(\displaystyle 13)/(\displaystyle 10)`

Explanation:

Hi there!

Slope-intercept form:
`y=mx+b` where
`m` is the slope and
`b` is the y-intercept (the value of y when x is 0)

1) Determine the slope (m)

`m=(\displaystyle y_2-y_1)/(\displaystyle x_2-x_1)` where two given points are
`(x_1,y_1)` and
`(x_2,y_2)`

Plug in the given points (15,2.2) and (5,1.6):

`m=(\displaystyle 1.6-2.2)/(\displaystyle 5-15)\\\\m=(\displaystyle -0.6)/(\displaystyle -10)\\\\m=(\displaystyle 0.6)/(\displaystyle 10)\\\\m=(\displaystyle 0.3)/(\displaystyle 5)\\\\m=(\displaystyle 3)/(\displaystyle 50)`

Therefore, the slope of the line is
`(\displaystyle 3)/(\displaystyle 50)`. Plug this into
`y=mx+b`:

`y=(\displaystyle 3)/(\displaystyle 50)x+b`

2) Determine the y-intercept (b)

`y=(\displaystyle 3)/(\displaystyle 50)x+b`

Plug in a given point and solve for b:

`1.6=(\displaystyle 3)/(\displaystyle 50)(5)+b\\\\1.6=(\displaystyle 3)/(\displaystyle 10)+b\\\\1.6-(\displaystyle 3)/(\displaystyle 10)=(\displaystyle 3)/(\displaystyle 10)+b-(\displaystyle 3)/(\displaystyle 10)\\\\(\displaystyle 13)/(\displaystyle 10)=b`

Therefore, the y-intercept is
`(\displaystyle 13)/(\displaystyle 10)`. Plug this back into
`y=(\displaystyle 3)/(\displaystyle 50)x+b`:

`y=(\displaystyle 3)/(\displaystyle 50)x+(\displaystyle 13)/(\displaystyle 10)`

I hope this helps!