yogirlmelody
Answered

Discover the best answers at Westonci.ca, where experts share their insights and knowledge with you. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

BIG QUESTION, 100 POINTS
Line p contains point (6, -5) and is perpendicular to line q. The equation for line q is y = 3x + 5. Write an equation for line p.
Find the slope of line q.
Find the slope of line p. (Write the negative reciprocal of the slope you found in Part I.)
Use the point given for line p and the slope you found in Part II to write an equation for line p in point-slope form: y - y1 = m (x - x1)
Use your equation from Part III to write an equation for line p in slope-intercept form: y = mx + b. Show your work.

Sagot :

semsee45

Answer:

[tex]\textsf{Slope of line q}: \quad 3[/tex]

[tex]\textsf{Slope of line p}:\quad -\dfrac{1}{3}[/tex]

[tex]\textsf{Equation of line p in slope-point form}: \quad y+5=-\dfrac{1}{3}(x-6)[/tex]

[tex]\textsf{Equation of line p in slope-intercept form}: \quad y=-\dfrac{1}{3}x-3[/tex]

Step-by-step explanation:

Slope-intercept form of a linear equation:  [tex]y = mx + b[/tex]

(where m is the slope and b is the y-intercept)

Given:

  • line q:  y = 3x + 5

Therefore, the slope of line q is 3.

As line p is perpendicular to line q, the slope of line p is the negative reciprocal of the slope of line q.

Therefore, the slope of line p is -1/3

Equation of line p, using the point-slope form, the slope of -1/3 and the point (6, -5):

[tex]\begin{aligned}y-y_1 &=m(x-x_1)\\\implies y-(-5) &=-\dfrac{1}{3}(x-6)\\y+5 &=-\dfrac{1}{3}(x-6)\end{aligned}[/tex]

Simplify to slope-intercept form:

[tex]\implies y=-\dfrac{1}{3}x-3[/tex]
  • y=3x+5

Slope of q:-

  • m=3

Perpendicular line's have slopes negative reciprocal to each other

Slope of p

  • -1/3

Passes through (6,-5)

Equation in point slope form

  • y+5=-1/3(x-6)
  • 3y+15=-x+6
  • 3y=-x-9
  • y=-1/3x-3
Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.