Writing Equations of Parallel Lines y 10 What is the slope of the line that is parallel
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
The slope of the parallel line to the given line is 
The equation of the parallel line to the given line and passes through the given point is y + 4 = (x + 2)
The y-intercept of the parallel line to the given line and passes through the given point is 
Step-by-step explanation:
The rule of the slope of the line that passes through points (x1, y1) and (x2, y2) is m =
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 lineThe slope-intercept form of the linear equation is y = m x + b, where m is the slope and b is the y-interceptParallel 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 = 
= 
=
∴ The slope of the given line is
∵ Parallel lines have the same slopes
∴ The slope of the parallel line to the given line is
∵ The parallel line passes through the point (-2, -4)
∴ x1 = -2 and y1 = -4
∵ m =
→ Substitute them in the point-slope form above
∵ y - (-4) = (x - (-2))
∴ y + 4 = (x + 2)
∴ The equation of the parallel line to the given line and passes through
the given point is y + 4 = (x + 2)
∵ m =
→ Substitute it in the slope-intercept form above
∴ y = x + b
→ To find b substitute x by -2 and y by -4 (coordinates the given point)
∵ -4 = (-2) + b
∴ -4 = 
+ b
→ Subtract from both sides
∴ = b
∵ b is the y-intercept
∴ The y-intercept of the parallel line to the given line and passes
through the given point is
How much
Step-by-step explanation
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