Question

What is the equation of a line that passes through (0.8) and (3,6)?

Answer 1

`y=(-2)/(3)x+8`

Explanation:

Hi there!

Linear equations are typically organized in slope-intercept form:
`y=mx+b` where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)

1) Determine the slope (m)

`m=(y_2-y_1)/(x_2-x_1)` where the given points
`(x_1,y_1)` are
`(x_2,y_2)`

Plug in the given points (0,8) and (3,6)

`m=(6-8)/(3-0)\\m=(-2)/(3)`

Therefore the slope of the line is
`(-2)/(3)`. Plug this into
`y=mx+b`:

`y=(-2)/(3)x+b`

2) Determine the y-intercept (b)

`y=(-2)/(3)x+b`

The y-intercept occurs when x=0. One of the given points is (0,8), so therefore, the y-intercept is 8. Plug this into
`y=(-2)/(3)x+b`:

`y=(-2)/(3)x+8`

I hope this helps!