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Question 7(Multiple Choice Worth 1 points) (02.04 MC) Write the equation of the line that passes through (3,-2) and is perpendicular to y=(3)/(4)x+6 y=-(4)/(3)x+(1)/(3) y=-(4)/(3)x+2 y=(3)/(4)x-(17)/(4) y=(4)/(3)x-6

Pergunta

Question 7(Multiple Choice Worth 1 points)
(02.04 MC)
Write the equation of the line that passes through (3,-2) and is perpendicular to y=(3)/(4)x+6
y=-(4)/(3)x+(1)/(3)
y=-(4)/(3)x+2
y=(3)/(4)x-(17)/(4)
y=(4)/(3)x-6

Question 7(Multiple Choice Worth 1 points) (02.04 MC) Write the equation of the line that passes through (3,-2) and is perpendicular to y=(3)/(4)x+6 y=-(4)/(3)x+(1)/(3) y=-(4)/(3)x+2 y=(3)/(4)x-(17)/(4) y=(4)/(3)x-6

Solução

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ZoraideProfissional · Tutor por 6 anos

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The correct answer is y=-\frac{4}{3}x+2.

Explicação

## Step 1
The is y=\frac{3}{4}x+6. The slope of this line is \frac{3}{4}.

## Step 2
The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. Therefore, the slope of the line perpendicular to the given line is -\frac{4}{3}.

## Step 3
The equation of a line in slope-intercept form is y=mx+b, where m is the slope and b is the y-intercept.

## Step 4
We know that the line passes through the point (3,-2). Substituting these values into the equation, we get -2=-\frac{4}{3}*3+b.

## Step 5
Solving for b, we get b=2.

## Step 6
Therefore, the equation of the line that passes through (3,-2) and is perpendicular to y=\frac{3}{4}x+6 is y=-\frac{4}{3}x+2.
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