how do you make an equation that is parallel to another equation?

how do you make an equation that is perpendicular to another equation?

please help and explain. Thank you.

Parallel equations have the same slope.

y = mx + b

Perpendicular equations have a reciprocal and opposite slope.

There is more to these questions than space allows here. Go to Khan Academy to view video's on how to do these equations.

To create an equation that is parallel to another equation, you need to follow these steps:

1. Identify the slope of the given equation: The slope is the coefficient of the variable with the highest power. For example, in the equation y = 2x + 3, the slope is 2.

2. Use the same slope for the new equation: Since parallel lines have the same slope, you can use the same slope in the new equation. For instance, if the given equation is y = 2x + 3, the new equation can be y = 2x + b, where b is any constant value.

Note: The constant value (b) can be different from the original equation since it represents the y-intercept and may vary.

To create an equation that is perpendicular to another equation, you should follow these steps:

1. Identify the slope of the given equation: Like before, the slope is the coefficient of the variable with the highest power. For example, in the equation y = 2x + 3, the slope is 2.

2. Determine the negative reciprocal of the given slope: The negative reciprocal is obtained by taking the negative of the given slope and then calculating its reciprocal. For example, if the given slope is 2, the negative reciprocal is -1/2.

3. Use the negative reciprocal slope for the new equation: Perpendicular lines have slopes that are negative reciprocals of each other. So, if the given equation is y = 2x + 3, the new equation would be y = (-1/2)x + b, where b is any constant value.

Again, remember that the constant value (b) may differ from the original equation, representing a different y-intercept.

These steps allow you to create equations parallel or perpendicular to a given equation by utilizing the concepts of slope and the relationship between slopes in parallel or perpendicular lines.