Chapter 4: Q. 700 (page 576)

Find the equation of each line. Write the equation in slope–intercept form.
parallel to the line $y = - \frac{2}{3} x - 1$ , containing the point $(- 3, 8)$

Short Answer

Expert verified

The equation in slope- intercept form is $y = \frac{- 2}{3} x + 6$ .

Step by step solution

Step 1. Given information

Line $y = - \frac{2}{3} x - 1$

Point $(- 3, 8)$

Step 2. Finding the slope of given line

As slope-intercept form is $y = m x + c$ .

Slope of given line $y = - \frac{2}{3} x - 1$ is $\frac{- 2}{3}$ .

Step 3. Finding slope of parallel line

As parallel lines have same slope, therefore, slope of parallel line is also $- \frac{2}{3}$ .

Step 4. Identifying the point

Given point $(- 3, 8)$

So, $x_{1} = - 3 y_{1} = 8$

Step 5. Substituting the values in point-slope form and simplifying

Point-slope form,

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

Putting values and simplifying ,

$y - y_{1} = m (x - x_{1}) y - 8 = \frac{- 2}{3} (x - (- 3)) y - 8 = \frac{- 2}{3} (x + 3)$

Step 6. Equation in slope-intercept form

$y - 8 = \frac{- 2}{3} (x + 3) y - 8 = \frac{- 2}{3} x - 2 y = \frac{- 2}{3} x - 2 + 8 y = \frac{- 2}{3} x + 6$

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Find the equation of each line. Write the equation in slope–intercept form.
parallel to the line $y = - \frac{2}{3} x - 1$ , containing the point $(- 3, 8)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the slope of given line

Step 3. Finding slope of parallel line

Step 4. Identifying the point

Step 5. Substituting the values in point-slope form and simplifying

Step 6. Equation in slope-intercept form

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Find the equation of each line. Write the equation in slope–intercept form.parallel to the line y=-23x-1, containing the point (-3,8)

Short Answer

Step by step solution

Step 1. Given information

Step 2. Finding the slope of given line

Step 3. Finding slope of parallel line

Step 4. Identifying the point

Step 5. Substituting the values in point-slope form and simplifying

Step 6. Equation in slope-intercept form

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find the equation of each line. Write the equation in slope–intercept form.
parallel to the line $y = - \frac{2}{3} x - 1$ , containing the point $(- 3, 8)$