Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Discover a wealth of knowledge from professionals across various disciplines on our user-friendly Q&A platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

Help Please! I dont understand these questions!
Directions: Write the equation of the line in point-slope form, then convert that equation to slope-intercept form. Show your work!

1. Write the equation of the line that is parallel to y = 2x + 4 and passes through the point (-4, -1).

2. Write the equation of the line that is parallel to y = ⅓x - 3 and passes through the point (3, -1).

3. Write the equation of the line that is perpendicular to y = ¾x - 1 and passes through the point (3, -3).

4. Write the equation of the line that is perpendicular to y = -x - 5 and passes through the point (7, 3).

Sagot :

unicorn3125

The point-slope form of the equation of line it's y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is the point the line passing through.

The slope-intercept form of the equation of line it's y = mx + b, where m is the slope and b is the y-intercept of the line.

1. Write the equation of the line that is parallel to y = 2x + 4 and passes through the point (-4, -1).

y=m₁x+b₁   ║   y=m₂x+b₂   ⇔    m₁ = m₂

{Two lines are parallel if  their slopes are equal}

y = 2x + 4  ⇒   m₁ = 2    ⇒    m₂ = 2

(-4, -1)  ⇒  x₁ = -4,  y₁ = -1

point-slope form:

y - (-1) = 2(x - (-4))

y + 1 = 2(x + 4)

y + 1 = 2x + 8               {subtact 1 from both sides}

y = 2x + 7         ←    slope-intercept form

2. Write the equation of the line that is parallel to y = ⅓x - 3 and passes through the point (3, -1).

y = ⅓x - 3  ⇒   m₁ =  ⅓    ⇒    m₂ =  ⅓

(3, -1)  ⇒  x₁ = 3,  y₁ = -1

point-slope form:

y - (-1) = ⅓(x - 3)

y + 1 = ⅓x - 1           {subtact 1 from both sides}

y = ⅓x - 2         ←    slope-intercept form

3. Write the equation of the line that is perpendicular to y = ¾x - 1 and passes through the point (3, -3).

y=m₁x+b₁   ⊥   y=m₂x+b₂   ⇔    m₁×m₂ = -1

{Two lines are perpendicular if the product of theirs slopes is equal -1}

y = ¾x - 1   ⇒   m₁ = ¾  

¾×m₂ = -1        ⇒    m₂ = -⁴/₃

(3, -3)  ⇒  x₁ = 3,  y₁ = -3

point-slope form:

y - (-3) =  -⁴/₃(x - 3)

y + 3 = -⁴/₃x + 4           {subtact 3 from both sides}

y = -⁴/₃x + 1         ←    slope-intercept form

4. Write the equation of the line that is perpendicular to y = -x - 5 and passes through the point (7, 3).

y = - x - 5   ⇒   m₁ = -1  

-1×m₂ = -1        ⇒    m₂ = 1

(7, 3)  ⇒  x₁ = 7,  y₁ = 3

point-slope form:

y - 3 =  -1(x - 7)

y - 3 = - x + 7           {add 3 to both sides}

y = - x + 10         ←    slope-intercept form

We hope this was helpful. Please come back whenever you need more information or answers to your queries. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.