Equation of Line from 2 Points Worksheets

Printable “Linear Equations” worksheets:
Linear Equations & Coordinate Plane
Slope of a Line (from 2 points)
Slope of a Line (from equation)
Graph Equation using Intercepts
Find the Equation of a Line from a Graph
Find the Equation of a Line from 2 Points
Constant Rate & Linear Equations

Examples, solutions, videos, and worksheets to help Grade 7 and Grade 8 learn how to write the equation of a line given two points or the slope and a point on the line.

How to write the equation of a line given two points or the slope and a point on the line?

To find the equation of a line given two points, you can use the point-slope form or the slope-intercept form.

Point-Slope Form:

1. Find the slope (m): Use the formula:
   m = (y2 - y1) / (x2 - x1)
   where (x1, y1) and (x2, y2) are the two points.
   
2. Choose one of the points: Select one of the given points.
   
3. Substitute into the point-slope form: Use the slope (m) and the chosen point (x1, y1) to write the equation in the form:
   y - y1 = m(x - x1)

Example:
Given the points (2, 3) and (5, 9), find the equation of the line.
Find the slope: m = (9 - 3) / (5 - 2) = 2
Choose the point (2, 3)
Substitute into point-slope form: y - 3 = 2(x - 2)
Rewrite as slope-intercept form: y = 2x -1

Slope-Intercept Form:

1. Find the slope (m): Use the formula as described above.
2. Substitute a point and the slope into y = mx + b: This will give you an equation with one unknown, b.
3. Solve for b: Solve the equation to find the y-intercept.
4. Write the equation: Substitute the values of m and b into y = mx + b.

Example:
Using the same points as before, (2, 3) and (5, 9):
Find the slope: m = 2
Substitute one point and the slope: 3 = 2(2) + b
Solve for b: 3 = 4 + b, b = -1
Write the equation: y = 2x - 1

In conclusion:

1. Both methods will give you the same equation.
2. Choose the method that you find easier or that is more convenient based on the given information.
3. Always check your answer by substituting the given points into the equation to make sure it satisfies the equation.

The following diagram shows how to write the equation of a line given two points.

Have a look at this video if you need to review how to find the equation of a line from two points.

• How To Find The Equation of Line from 2 Points

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More Equation of Line from 2 Points Worksheets

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(Answers on the second page.)
Equation of Line from 2 Points Worksheet #1
Equation of Line from 2 Points Worksheet #2
Equation of Line from 2 Points Worksheet #3
Equation of Line from 2 Points Worksheet #4
Equation of Line from 2 Points Worksheet #5

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