How to Write Linear Equations? (+FREE Worksheet!)

Related Topics

• How to Find Midpoint
• How to Find Slope
• How to Graph Linear Inequalities
• How to Find Distance of Two Points
• How to Graph Lines by Using Standard Form

Step by step guide to writing linear equations

• The equation of a line in slope intercept form is: $\color{blue}{y=mx+b}$
• Identify the slope.
• Find the $y$–intercept. This can be done by substituting the slope and the coordinates of a point $(x, y)$ on the line.

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Writing Linear Equations – Example 1:

What is the equation of the line that passes through $(1, -2)$ and has a slope of $6$?

Solution:

The general slope-intercept form of the equation of a line is $y=mx+b$, where $m$ is the slope and $b$ is the $y$-intercept.
By substitution of the given point and given slope, we have: $-2=(6)(1)+b → -2=6+b$
So, $b= -2-6=-8$, and the required equation is $y=6x-8$.

Writing Linear Equations – Example 2:

Write the equation of the line through $(1, 1)$ and $(-1, 3)$.

Solution:

Slop $= \frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{3- 1}{-1- 1}=\frac{2}{-2}=-1 → m=-1$
To find the value of $b$, you can use either point. The answer will be the same: $y=-x+b$
$(1,1) →1=-1+b→ 1+1=b → b=2$
$(-1,3)→3=-(-1)+b→3-1=b → b=2$
The equation of the line is: $y=-x+2$

Writing Linear Equations – Example 3:

What is the equation of the line that passes through $(2,–2)$ and has a slope of $7$?

Solution:

The general slope-intercept form of the equation of a line is $y=mx+b$, where $m$ is the slope and $b$ is the $y-$intercept.
By substitution of the given point and given slope, we have: $-2=(7)(2)+b → -2=14+b$
So, $b= –2-14=-16$, and the required equation is $y=7x-16$.

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Writing Linear Equations – Example 4:

Write the equation of the line through $(2,1)$ and $(-1,4)$.

Solution:

Slop $= \frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{4- 1}{-1- 2}=\frac{3}{-3}=-1 → m= -1$
You can use either point to find the value of $b$. The answer will be the same: $y= -x+b$
$(2,1) →1=-2+b→1+2=b → b=3$
$(-1,4)→4=-(-1)+b→4-1=b → b=3$
The equation of the line is: $y=-x+3$

Exercises for Writing Linear Equations

Write the slope–intercept form of the equation of the line through the given points.

1. $\color{blue}{through: (– 4, – 2), (– 3, 5)}$
2. $\color{blue}{through: (5, 4), (– 4, 3) }$
3. $\color{blue}{through: (0, – 2), (– 5, 3) }$
4. $\color{blue}{through: (– 1, 1), (– 2, 6) }$
5. $\color{blue}{through: (0, 3), (– 4, – 1) }$
6. $\color{blue}{through: (0, 2), (1, – 3) }$

Download Writing Linear Equations Worksheet

1. $\color{blue}{y = 7x + 26}$
2. $\color{blue}{y = \frac{1}{9} x + \frac{31}{9}}$
3. $\color{blue}{y =\space – x – 2}$
4. $\color{blue}{y =\space –5x – 4}$
5. $\color{blue}{y = x + 3}$
6. $\color{blue}{y =\space – 5x + 2}$

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