Question

Write an equation of the line that passes through the points (3.2) and (6,11). Show your work!

Answer 1

`y=3x-7`

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 points given are
`(x_1,y_1)` and
`(x_2,y_2)`

Points (3,2) and (6,11)

`=(11-2)/(6-3)\\=(9)/(3)\\= 3`

Therefore, the slope of the line is 3. Plug this into
`y=mx+b`:

`y=3x+b`

2) Determine the y-intercept (b)

`y=3x+b`

Plug in one of the given points and solve for b

`2=3(3)+b\\2=9+b`

Subtract 9 from both sides

`2-9=9+b-9\\-7=b`

Therefore, the y-intercept of the line is -7. Plug this back into
`y=3x+b`:

`y=3x-7`

I hope this helps!