Find the Equation of the Solution to Through the 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
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 (shown immediately below)
Step 1 Step 2Substitute the given point (1, 7) into the x and y values
$ y = \red 3 x + b \\ 7 = \red 3 (1) + b $
Solve for b (the y-intercept)
$ \begin{align*} 7 &= 3 (1) + b \\ 7 &= 3 + b \\ -3 & -3 \\ \hline \\ 4 &= b \\ \end{align*} $
Step 4Substitute 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 y - y 1 = m(x - x 1)
y - y 1 = 3(x - x 1)
Substitute the given point (1, 7) into the x 1 and y 1 values y - 7= 3(x - 1)
Practice Problems
Problem 1 - Method 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 2
Substitute the given point $$(5, 9) $$ into the x and y values.
$ y = 4x + b \\ 9 = 4(5) + b $
Step 3
$ \begin{align*} 9 &= 4 (5) + b \\ 9 &= 20 + b \\ -20 & -20 \\ \hline \\ -11 &= b \\ \end{align*} $
Problem 1 - Method 2
What is the equation of line parallel to y = 4x + 3 and through the point (5, 9)?
Using Point Slope Form - Method 2
Step 1
y - y 1 = m(x - x 1)
y - y 1 = 4(x - x 1)
Step 2
Substitute the given point (5, 9) into the x 1 and y 1 values.
Problem 2 - Method 1
What is the equation of line parallel to y = ¾x +22 and through the point (-8, 11)?
Slope Intercept Form - Method 1
Step 2
Substitute the given point (-8, 11) into the x and y values.
y = ¾x + b
11 = ¾(-2) + b
Step 3
Problem 2 - Method 2
What is the equation of line parallel to y = ¾x + 22 and through the point (-8, 11)?
Using Point Slope Form - Method 2
Step 1
y - y 1 = m(x - x 1)
y - y 1 = ¾(x - x 1)
Step 2
Substitute the given point (-8, 11) into the x 1 and y 1 values.
Problem 3 - Method 1
What is the equation of line parallel to y = -¼x + 21 and through the point (32, -4)?
Slope Intercept Form - Method 1
Step 2
Substitute the given point (32, -4) into the x and y values.
y = -¼x + b
-4 = -¼(32) + b
Step 3
Problem 3 - Method 2
What is the equation of line parallel to y = -¼x + 21 and through the point (32, -4)?
Using Point Slope Form - Method 2
Step 1
y - y 1 = m(x - x 1)
y - y 1 = - ¼(x - x 1)
Step 2
Substitute the given point (32, -4) into the x 1 and y 1 values.
Find the Equation of the Solution to Through the Point
Source: https://www.mathwarehouse.com/algebra/linear_equation/write-equation/equation-of-line-parallel-through-point.php