Chapter 3: Q 3.61. (page 288)

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 is $y = - \frac{1}{3} x + \frac{10}{3}$ .

Step by step solution

Step 1. Find the slope of the given line

The given line is: $y = 3 x + 1$

The line is in slope-intercept form. Therefore, its slope is:

$m = 3$

Step 2. Find the slope of the perpendicular line and identify the point

The slopes of perpendicular lines are negative reciprocals.

Therefore, the slope of the perpendicular line is:

$m_{1} = - \frac{1}{3}$

And the given point is $(4, 2)$ .

$(x_{1}, y_{1}) = (4, 2)$

Step 3. Substitute the values into the point-slope form

The point-slope form is:

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

Step 4. Write the equation in slope-intercept form.

The slope-intercept form of the perpendicular line is $y = - \frac{1}{3} x + \frac{10}{3}$ .

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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. Find the slope of the given line

Step 2. Find the slope of the perpendicular line and identify the point

Step 3. Substitute the values into the point-slope form

Step 4. Write the equation in slope-intercept form.

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

Short Answer

Step by step solution

Step 1. Find the slope of the given line

Step 2. Find the slope of the perpendicular line and identify the point

Step 3. Substitute the values into the point-slope form

Step 4. Write the equation in slope-intercept form.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Geometry

Calculus

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.