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

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:

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  

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step-by-step explanation:

the infinity sign

step-by-step explanation: