Question

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

Answer 1

What is the slope of the line that is parallel to the given line and passes through the given point?

✔ –1/4

What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the given point?

✔ y + 4 = –1/4(x + 2)

What is the y-intercept of the line that is parallel to the given line and passes through the given point?

✔ –9/2

Explanation:

Answer 2

The slope of the parallel line to the given line is
`-(1)/(4)`

The equation of the parallel line to the given line and passes through the given point is y + 4 =
`-(1)/(4)` (x + 2)

The y-intercept of the parallel line to the given line and passes through the given point is
`-(9)/(2)`

Explanation:

• The rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m =
  `(y2-y1)/(x2-x1)`

• 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 =
`(8-6)/(-6-2)` =
`(2)/(-8)` =
`-(1)/(4)`

∴ The slope of the given line is
`-(1)/(4)`

∵ Parallel lines have the same slopes

∴ The slope of the parallel line to the given line is
`-(1)/(4)`

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

∴ x1 = -2 and y1 = -4

∵ m =
`-(1)/(4)`

→ Substitute them in the point-slope form above

∵ y - (-4) =
`-(1)/(4)` (x - (-2))

∴ y + 4 =
`-(1)/(4)` (x + 2)

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

the given point is y + 4 =
`-(1)/(4)` (x + 2)

∵ m =
`-(1)/(4)`

→ Substitute it in the slope-intercept form above

∴ y =
`-(1)/(4)` x + b

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

∵ -4 =
`-(1)/(4)`(-2) + b

∴ -4 =
`(1)/(2)` + b

→ Subtract
`(1)/(2)` from both sides

∴
`-(9)/(2)` = b

∵ b is the y-intercept

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

through the given point is
`-(9)/(2)`