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

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.

Video Tutorial on Equation of Line Parallel and Through A Point

Example 1

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

Method 1: Using Slope Intercept Form

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

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	y − y 1 = m(x − x1) y − y1 = 3(x − x1)
Step 2) Substitute the given point (1,7) into the x1 and y1 values	y − 7= 3(x − 1)

Problem 1)

What is the equation of line parallel to y = 4x + 3 and through the point (5 ,9)?

Using Slope Intercept Form (Method 1)

Step 1

Step 1) Substitute slope from original line (4 in this case) into the slope intercept equation.

y = 4x +b

Step 2

Step 2) Substitute the given point (5,9) into the x and y values

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

Step 3

Step 3) Solve for b (the y-intercept)

Step 4

Step 4) Substitute this value for 'b' in the slope intercept form equation

y =4x − 20

Using Point Slope Form (Method 2)


Problem 1)

What is the equation of line parallel to y = 4x + 3 and through the point (5 ,9)?

Step 1

Step 1) Substitute the slope from original line (4 in this case) into the point slope equation

y − y 1 = m(x − x1) y − y1 = 4(x − x1)

Step 2

Step 2) Substitute the given point (5,9) into the x1 and y1 values

y − 5= 4(x − 9)

Problem 2)

What is the equation of line parallel to y = ¾x +22 and through the point (-8 , 11)?

Slope Intercept Form (Method 1)

Step 1

Step 1) Substitute slope from original line (¾ in this case) into the slope intercept equation.

y = ¾x +22

Step 2

Step 2) Substitute the given point (-8, 11) into the x and y values

y = ¾x +b 11 = ¾(-2) +b

Step 3

Step 3) Solve for b (the y-intercept)

Step 4

Step 4) Substitute this value for 'b' in the slope intercept form equation

y =¾x + 17

Using Point Slope Form Method 2


Problem 2)

What is the equation of line parallel to y = ¾x +22 and through the point (-8 , 11)?

Step 1

Step 1) Substitute the slope from original line (¾ in this case) into the point slope equation

y − y 1 = m(x − x1) y − y1 = ¾(x − x1)

Step 2

Step 2) Substitute the given point (-8,11) into the x1 and y1 values

y − 11= ¾(x + 8)

Problem 3)

What is the equation of line parallel to y = −¼x + 21 and through the point (32 , -4)?

Slope Intercept Form (Method 1)

Step 1

Step 1) Substitute slope from original line (-¼ in this case) into the slope intercept equation.

y = -¼x +22

Step 2

Step 2) Substitute the given point ( 32, -4) into the x and y values

y = -¼x +b -4 = -¼( 32) +b

Step 3

Step 3) Solve for b (the y-intercept)

Step 4

Step 4) Substitute this value for 'b' in the slope intercept form equation

y = −¼x + 4

Using Point Slope Form Method 2


Problem 3)

What is the equation of line parallel to y = −¼x + 21 and through the point (32 , -4)?

Step 1

Step 1) Substitute the slope from original line (−¼ in this case) into the point slope equation

y − y 1 = m(x − x1) y − y1 = − ¼(x − x1)

Step 2

Step 2) Substitute the given point (32, -4) into the x1 and y1 values

y + 4 = − ¼(x − 32)