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

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)

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1 year 2021-09-02T07:17:25+00:00 1 Answers 0 views 0

$$x-2y=-12$$

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!