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zhannawk [14.2K]
1 year ago
6

The slope-intercept form given (6,-5) & perpendicular to -5x - 7y = -17.

Mathematics
1 answer:
tatuchka [14]1 year ago
8 0

Answer:

y=\dfrac{7}{5}x-\dfrac{67}{5}

Step-by-step explanation:

<u>Slope-intercept form of a linear equation:</u>

 y=mx+b

where:

  • m is the slope.
  • b is the y-intercept.

<u>Rearrange</u> the given equation so that it is in <u>slope-intercept form</u>:

\implies -5x-7y=-17

\implies -7y=5x-17

\implies y=-\dfrac{5}{7}x+\dfrac{17}{7}

Therefore, the slope of the given equation is -⁵/₇.

If two lines are <u>perpendicular</u> to each other (at right angles), the <u>product of their slopes</u> will be -1.  Therefore, their slopes will be negative reciprocals of each other.

Therefore, the slope of the line perpendicular to the given equation is:

\sf m=\dfrac{7}{5}

<u>Substitute</u> the found <u>slope</u> and the <u>given point</u> (6, -5) into the <u>slope-intercept formula</u> and solve for b:

\implies -5=\dfrac{7}{5}(6)+b

\implies -5=\dfrac{42}{5}+b

\implies b=-\dfrac{67}{5}

<u>Substitute</u> the found slope and the found value of b into the <u>slope-intercept formula</u> to create the equation for the <u>perpendicular line</u>:

\implies y=\dfrac{7}{5}x-\dfrac{67}{5}

Learn more about slope-intercept form here:

brainly.com/question/27317293

brainly.com/question/27926846

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Note :- Kindly view the answer from web , if you're not able to see the full answer from here ;

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