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Write the equation of the line that has the indicated slope and contains the indicated point. Express the final equation in standard form.**
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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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Mathematics
1 year
2021-09-02T07:17:25+00:00
2021-09-02T07:17:25+00:00 1 Answers
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## Answers ( )

Answer:[tex]x-2y=-12[/tex]

Step-by-step explanation:Hi there!

1) Determine the equation of the line in slope-intercept formLinear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when x is 0)

Plug in the slope [tex]\frac{1}{2}[/tex]

[tex]y=\frac{1}{2}x+b[/tex]

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

[tex]9=\frac{1}{2}(6)+b\\9=3+b[/tex]

Subtract 3 from both sides

[tex]9-3=3+b-3\\6=b[/tex]

Plug 6 back into [tex]y=\frac{1}{2}x+b[/tex]

[tex]y=\frac{1}{2}x+6[/tex]

2) Rearrange the equation into standard formStandard form: [tex]Ax+By=C[/tex] where A, B and C are integers and A is typically positive

[tex]y=\frac{1}{2}x+6[/tex]

Multiply both sides by 2 to remove the fraction

[tex]2y=1x+12\\2y=x+12[/tex]

Subtract x from both sides to isolate 12 as C

[tex]2y-x=x+12-x\\2y-x=12\\-x+2y=12[/tex]

Multiply both sides by -1 to make A positive

[tex]x-2y=-12[/tex]

I hope this helps!