Parallel Lines Worksheets

Examples, solutions, videos, and worksheets to help grade 7 students learn how to find the equation of a line passing through a given point and parallel to the given equation.

How to find the equation of Parallel Lines?

There are three sets of Parallel Lines worksheets:

• Equation given in slope-intercept form
• Equation given in standard form
• Equation in both forms

To find the equation of a line that is parallel to a given line, you need the slope of the given line and the point at which the parallel line should pass. Parallel lines have the same slope, so if you know the slope of the given line, you can use it to find the equation of the parallel line.

Here are the steps to find the equation of a parallel line:

1. Determine the slope of the given line. The slope (m) can be found by rearranging the equation into the slope-intercept form (y = mx + b) and identifying the coefficient of x (m).
2. Use the same slope (m) to create the equation of the parallel line. y = mx + c
3. To find the specific equation of the parallel line, you need a point through which it passes. If you have a point (x₁, y₁) that the parallel line must pass through, substitute these coordinates into the equation:
   y = mx + c
4. Solve for c to find the specific equation of the parallel line.

Example:
Find the equation of a line parallel to y = 3x + 2 that passes through the point (4, 5).

1. Start with the given line: y = 3x + 2.
2. Use the same slope (m = 3) to create the equation of the parallel line: y = 3x + c.
3. Substitute the point (4, 5) into the equation: 5 = 3(4) + c.
4. Solve for c: c = 5 - 3(4) = 5 - 12 = -7.

The equation of the parallel line is: y = 3x - 7.

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