Question

Write the equation of the line that has the indicated slope and contains the indicated point. Express the final equation in standard form.

m = 1/2, (6, 9)

Answer 1

`x-2y=-12`

Explanation:

Hi there!

1) Determine the equation of the line in slope-intercept form

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 x is 0)

Plug in the slope
`(1)/(2)`

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

Plug in the given point (6,9) and solve for b

`9=(1)/(2)(6)+b\\9=3+b`

Subtract 3 from both sides

`9-3=3+b-3\\6=b`

Plug 6 back into
`y=(1)/(2)x+b`

`y=(1)/(2)x+6`

2) Rearrange the equation into standard form

Standard form:
`Ax+By=C` where A, B and C are integers and A is typically positive

`y=(1)/(2)x+6`

Multiply both sides by 2 to remove the fraction

`2y=1x+12\\2y=x+12`

Subtract x from both sides to isolate 12 as C

`2y-x=x+12-x\\2y-x=12\\-x+2y=12`

Multiply both sides by -1 to make A positive

`x-2y=-12`

I hope this helps!