Answered

Get expert insights and reliable answers to your questions on IDNLearn.com. Get prompt and accurate answers to your questions from our community of knowledgeable experts.

Writing Equations of Parallel Lines
y
10
What is the slope of the line that is parallel to the given
line and passes through the given point?
8
6
What is the equation, in point-slope form, of the line
that is parallel to the given line and passes through the
given point?
4.
2
-10 -8 6 4
What is the y-intercept of the line that is parallel to the
given line and passes through the given point?
2
4.
6
8
10
-2
-2
4
-6
-8
-10

Writing Equations Of Parallel Lines Y 10 What Is The Slope Of The Line That Is Parallel To The Given Line And Passes Through The Given Point 8 6 What Is The Equ class=

Sagot :

Ashraf82idn

Answer:

The slope of the parallel line to the given line is [tex]-\frac{1}{4}[/tex]

The equation of the parallel line to the given line and passes through the given point is y + 4 =  [tex]-\frac{1}{4}[/tex] (x + 2)

The y-intercept of the parallel line to the given line and passes through the given point is  [tex]-\frac{9}{2}[/tex]

Step-by-step explanation:

  • The rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m = [tex]\frac{y2-y1}{x2-x1}[/tex]
  • The point-slope form of the linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line
  • The slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-intercept
  • Parallel lines have the same slopes and different y-intercepts

In the given figure

∵ The given line passes through points (2, 6) and (-6, 8)

∴ x1 = 2 and y1 = 6

∴ x2 = -6 and y2 = 8

→ Substitute them in the rule of the slope above to find it

∵ m = [tex]\frac{8-6}{-6-2}[/tex] = [tex]\frac{2}{-8}[/tex] = [tex]-\frac{1}{4}[/tex]

∴ The slope of the given line is [tex]-\frac{1}{4}[/tex]  

∵ Parallel lines have the same slopes

∴ The slope of the parallel line to the given line is [tex]-\frac{1}{4}[/tex]

∵ The parallel line passes through the point (-2, -4)

∴ x1 = -2 and y1 = -4

∵ m = [tex]-\frac{1}{4}[/tex]

→ Substitute them in the point-slope form above

∵ y - (-4) = [tex]-\frac{1}{4}[/tex] (x - (-2))

∴ y + 4 =  [tex]-\frac{1}{4}[/tex] (x + 2)

∴ The equation of the parallel line to the given line and passes through

   the given point is y + 4 =  [tex]-\frac{1}{4}[/tex] (x + 2)

∵ m = [tex]-\frac{1}{4}[/tex]

→ Substitute it in the slope-intercept form above

∴ y =  [tex]-\frac{1}{4}[/tex] x + b

→ To find b substitute x by -2 and y by -4 (coordinates the given point)

∵ -4 = [tex]-\frac{1}{4}[/tex](-2) + b

∴ -4 = [tex]\frac{1}{2}[/tex] + b

→ Subtract  [tex]\frac{1}{2}[/tex]  from both sides

∴ [tex]-\frac{9}{2}[/tex] = b

∵ b is the y-intercept

∴ The y-intercept of the parallel line to the given line and passes

   through the given point is  [tex]-\frac{9}{2}[/tex]

Your participation means a lot to us. Keep sharing information and solutions. This community grows thanks to the amazing contributions from members like you. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.