By looking at two linear equations, how can you tell that the corresponding lines are parallel?
they will have the same slope
y=mx+b
y=2x+2 and y=2x+4 are parallel
To determine if two linear equations represent parallel lines, you need to compare their slopes. The slope of a line represents how steeply it rises or falls.
In general, if two lines have the same slope, they are parallel. Mathematically, if two equations have the form y = mx + b, where "m" represents the slope, and the values of "m" are equal, then the lines are parallel.
To find the slope of a line given its equation, you can use the following approach:
1. Look at the equation of the line and identify the coefficient of the x-term. Let's call it "a".
2. The slope, "m", is equal to the coefficient "a" of the x-term.
For example, consider the equations:
Equation 1: y = 2x + 1
Equation 2: y = 2x - 3
Both equations have a coefficient of 2 for the x-term, which means their slopes are equal (m = 2). Therefore, the lines represented by these equations are parallel.
Remember, if the coefficients of the x-term are different, then the lines will have different slopes and will not be parallel.