Chapter 4: Q. 131 (page 534)

Find an equation of a line perpendicular to the line $y = 3 x + 1$ that contains the point $(4, 2)$ . Write the equation in slope-intercept form.

Short Answer

Expert verified

The equation of the line in slope-intercept form is $y = - \frac{x}{3} + \frac{10}{3}$ .

Step by step solution

Step 1. Given Information.

The equation of the line, $y = 3 x + 1$ .

The point is, $(4, 2)$ .

Step 2. Finding the slope.

The slope-intercept form is,

$y = m x + b$ .

Comparing the equation of the line $y = 3 x + 1$ ,

$m_{1} = 3$

When two lines are perpendicular,

$m_{1} \times m_{2} = - 1 \Rightarrow 3 \times m_{2} = - 1 \Rightarrow m_{2} = - \frac{1}{3}$

Step 3. Equation of the line.

The point-slope form is,

$(y - y_{1}) = m (x - x_{1})$

Inputting the values,

$(y - 2) = - \frac{1}{3} (x - 4) y - 2 = - \frac{x}{3} + \frac{4}{3} y = - \frac{x}{3} + \frac{10}{3}$

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Find an equation of a line perpendicular to the line $y = 3 x + 1$ that contains the point $(4, 2)$ . Write the equation in slope-intercept form.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the slope.

Step 3. Equation of the line.

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Find an equation of a line perpendicular to the liney=3x+1that contains the point(4,2). Write the equation in slope-intercept form.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Finding the slope.

Step 3. Equation of the line.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Geometry

Calculus

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find an equation of a line perpendicular to the line $y = 3 x + 1$ that contains the point $(4, 2)$ . Write the equation in slope-intercept form.