Chapter 4: Q21. (page 271)

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

Short Answer

Expert verified

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

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:

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

Step 2. Write the equation of the line that passes through the point −3,−1 and has the slope 25.

The slope of the line is $\frac{2}{5}$ . Therefore, the value of $m$ is $\frac{2}{5}$ .

The given point is $(- 3, - 1)$ . Therefore, the values of $x_{1}$ and $y_{1}$ are $- 3$ and $- 1$ respectively.

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

role="math" localid="1647414515033" $y - y_{1} = m (x - x_{1}) y - (- 1) = \frac{2}{5} (x - (- 3)) y + 1 = \frac{2}{5} (x + 3) y + 1 = \frac{2}{5} x + \frac{6}{5} y = \frac{2}{5} x + \frac{6}{5} - 1 y = \frac{2}{5} x + \frac{6 - 5}{5} y = \frac{2}{5} x + \frac{1}{5}$

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

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

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 −3,−1 and has the slope 25.

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Write an equation of the line that passes through the given point and has the given slope.−3,−1, slope25

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 −3,−1 and has the slope 25.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Statistics

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Pure Maths

Study anywhere. Anytime. Across all devices.

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