﻿ Write Equation of Line parallel to a given line and point-- a You-Tube style demonstration and walk through with extra practice...

# Write the Equation of a Line Parallel to a line and through a point

Video Demonstration

Students are often asked to find the equation of a line that is parallel to another line and that passes through a point. Watch the video tutorial below to understand how to do these problems and, if you want, download this free worksheet if you want some extra practice.

### Example

#### Method 1: Using Slope Intercept Form

What is the equation of line parallel to y = 3x + 5 and through the point (1, 7)?

Many students are more comfortable using slope intercept form but this kind of problem is actually much easier , using point slope form (which is right below this work)

Step 1

Substitute the slope from original line (3 in this case) into the equation of the line y = 3x + b

Step 2

Substitute the given point (1,7) into the x and y values 7 = 3(1) + b

Step 3

Solve for b (the y-intercept)

Step 4

Substitute this value for 'b' in the slope intercept form equation y = 3x + 4

#### Method 2: Using Post Slope Form

What is the equation of line parallel to y = 3x + 5 and through the point (1, 7)?

If you're comfortable with point slope form , this is the way to go! Just look how little work there is to do! In fact, all that you have to do is substitute twice!

Step 1

Substitute the slope from original line (3 in this case) into the point slope equation yy1 = m(xx1)
yy1 = 3(xx1)

Step 2

Substitute the given point (1,7) into the x1 and y1 values y − 7= 3(x − 1)

### Practice Problems

Step 1

Substitute slope from original line (4 in this case) into the slope intercept equation.

y = 4x +b

Step 2

Substitute the given point (5,9) into the x and y values

y = 4x +b
9 = 4(5) +b

Step 3

Solve for b (the y-intercept)

Step 4

Substitute this value for 'b' in the slope intercept form equation

y =4x − 20

Step 1

Substitute the slope from original line (4 in this case) into the point slope equation

yy1 = m(xx1)
yy1 = 4(xx1)

Step 2

Substitute the given point (5,9) into the x1 and y1 values

y − 5= 4(x − 9)

Step 1

Substitute slope from original line (¾ in this case) into the slope intercept equation

y = ¾x +22

Step 2

Substitute the given point (-8, 11) into the x and y values

y = ¾x +b
11 = ¾(-2) +b

Step 3

Solve for b (the y-intercept)

Step 4

Substitute this value for 'b' in the slope intercept form equation

y =¾x + 17

Step 1

Substitute the slope from original line (¾ in this case) into the point slope equation

yy1 = m(xx1)
yy1 = ¾(xx1)

Step 2

Substitute the given point (-8,11) into the x1 and y1 values

y − 11= ¾(x + 8)

Step 1

Substitute slope from original line (-¼ in this case) into the slope intercept equation

y = x +22

Step 2

Substitute the given point ( 32, -4) into the x and y values

y = -¼x +b
-4 = -¼( 32) +b

Step 3

Solve for b (the y-intercept)

Step 4

Substitute this value for 'b' in the slope intercept form equation

y = −¼x + 4

Step 1

Substitute the slope from original line (−¼ in this case) into the point slope equation

yy 1 = m(xx1)
yy1 = − ¼(xx1)

Step 2

Substitute the given point (32, -4) into the x1 and y1 values

y + 4 = − ¼(x − 32)

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