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

Answer:

$x-2y=-12$

Step-by-step 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 $\frac{1}{2}$

$y=\frac{1}{2}x+b$

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

$9=\frac{1}{2}(6)+b\\9=3+b$

Subtract 3 from both sides

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

Plug 6 back into $y=\frac{1}{2}x+b$

$y=\frac{1}{2}x+6$

2) Rearrange the equation into standard form

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

$y=\frac{1}{2}x+6$

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!