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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 :

Ashraf82

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]

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