QuestionFind the slope of a line perpendicular to $y - 2 = 3x$ . Options: A. -3 B. $-\frac{1}{3}$ C. $\frac{1}{3}$ D. 2 E. 3

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given by $y-=3x$ . . We are looking for the slope of a line perpendicular to the given line.

STEP 2

First, we need to find the slope of the given line. The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope.

STEP 3

Rewrite the given equation in slope-intercept form.
$y =3x +2$

STEP 4

From the equation, we can see that the slope of the given line is3.

STEP 5

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.
$m_{\perp} = -\frac{1}{m}$

STEP 6

Substitute the value of the slope of the given line into the formula to find the slope of the line perpendicular to it.
$m_{\perp} = -\frac{1}{3}$ Therefore, the slope of the line perpendicular to the line defined by $y-2=3x$ is $-\frac{1}{3}$ , which corresponds to option B.

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QuestionFind the slope of a line perpendicular to $y - 2 = 3x$ . Options: A. -3 B. $-\frac{1}{3}$ C. $\frac{1}{3}$ D. 2 E. 3

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given by $y-=3x$ . . We are looking for the slope of a line perpendicular to the given line.

STEP 2

First, we need to find the slope of the given line. The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope.

STEP 3

Rewrite the given equation in slope-intercept form.
$y =3x +2$

STEP 4

From the equation, we can see that the slope of the given line is3.

STEP 5

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.
$m_{\perp} = -\frac{1}{m}$

STEP 6

Substitute the value of the slope of the given line into the formula to find the slope of the line perpendicular to it.
$m_{\perp} = -\frac{1}{3}$ Therefore, the slope of the line perpendicular to the line defined by $y-2=3x$ is $-\frac{1}{3}$ , which corresponds to option B.

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QuestionFind the slope of a line perpendicular to y−2=3xy - 2 = 3xy−2=3x. Options: A. -3 B. −13-\frac{1}{3}−31​ C. 13\frac{1}{3}31​ D. 2 E. 3

Studdy Solution

STEP 1

Assumptions1. The equation of the line is given by y−=3xy-=3xy−=3x. . We are looking for the slope of a line perpendicular to the given line.

STEP 2

First, we need to find the slope of the given line. The slope-intercept form of a linear equation is y=mx+by = mx + by=mx+b, where mmm is the slope.

STEP 3

Rewrite the given equation in slope-intercept form.y=3x+2y =3x +2y=3x+2

STEP 4

From the equation, we can see that the slope of the given line is3.

STEP 5

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.m⊥=−1mm_{\perp} = -\frac{1}{m}m⊥​=−m1​

STEP 6

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QuestionFind the slope of a line perpendicular to $y - 2 = 3x$ . Options: A. -3 B. $-\frac{1}{3}$ C. $\frac{1}{3}$ D. 2 E. 3

Assumptions1. The equation of the line is given by $y-=3x$ . . We are looking for the slope of a line perpendicular to the given line.

First, we need to find the slope of the given line. The slope-intercept form of a linear equation is $y = mx + b$ , where $m$ is the slope.

Rewrite the given equation in slope-intercept form.
$y =3x +2$

The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line.
$m_{\perp} = -\frac{1}{m}$