Q22. Write an equation of the line th... [FREE SOLUTION]

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Algebra 1

Carter, Cuevas, Day, Holiday, Luchin

$Math Studyset 91影视 Explanations$ Math

Student Edition 路 801 pages

ISBN: 9780078884801

Chapter 4: Q22. (page 271)

Write an equation of the line that passes through the given point and has the given slope.
$(5, 鈭� 2)$ , slope $鈭� \frac{1}{3}$

Short Answer

Expert verified

The equation of the line that passes through the point $(5, 鈭� 2)$ and has the slope $鈭� \frac{1}{3}$ is $y = \frac{鈭� 1}{3} x 鈭� \frac{1}{3}$ .

Step by step solution

Step 1. Write the equation of the line that passes through the point x1,y1 and has the slope m.

The equation of the line that passes through the point $(x_{1}, y_{1})$ and has the slope $m$ is given by:

$y 鈭� y_{1} = m (x 鈭� x_{1})$

Step 2. Write the equation of the line that passes through the point 5,−2 and has the slope −13.

The slope of the line is $鈭� \frac{1}{3}$ . Therefore, the value of $m$ is $鈭� \frac{1}{3}$ .

The given point is $(5, 鈭� 2)$ . Therefore, the values of $x_{1}$ and $y_{1}$ are 5 and $鈭� 2$ respectively.

Now substitute $鈭� \frac{1}{3}$ for $m$ , 5 for $x_{1}$ and $鈭� 2$ for $y_{1}$ in the equation $y 鈭� y_{1} = m (x 鈭� x_{1})$ to find the equation of the line.

$y 鈭� y_{1} = m (x 鈭� x_{1}) y 鈭� (鈭� 2) = 鈭� \frac{1}{3} (x 鈭� 5) y + 2 = \frac{鈭� 1}{3} x + \frac{5}{3} y = \frac{鈭� 1}{3} x + \frac{5}{3} 鈭� 2 y = \frac{鈭� 1}{3} x + \frac{5 鈭� 6}{3} y = \frac{鈭� 1}{3} x 鈭� \frac{1}{3}$

Therefore, the equation of the line that passes through the point $(5, 鈭� 2)$ and has the slope $鈭� \frac{1}{3}$ is $y = \frac{鈭� 1}{3} x 鈭� \frac{1}{3}$ .

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91影视

Write an equation of the line that passes through the given point and has the given slope.
$(5, 鈭� 2)$ , slope $鈭� \frac{1}{3}$

Short Answer

Step by step solution

Step 1. Write the equation of the line that passes through the point x1,y1 and has the slope m.

Step 2. Write the equation of the line that passes through the point 5,−2 and has the slope −13.

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91影视

Write an equation of the line that passes through the given point and has the given slope.5,鈭�2, slope鈭�13

Short Answer

Step by step solution

Step 1. Write the equation of the line that passes through the point x1,y1 and has the slope m.

Step 2. Write the equation of the line that passes through the point 5,−2 and has the slope −13.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Statistics

Geometry

Applied Mathematics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

Write an equation of the line that passes through the given point and has the given slope.
$(5, 鈭� 2)$ , slope $鈭� \frac{1}{3}$