Determine whether each pair of equations represents parallel lines 3x=5y-2 and 10y=4-6x
To determine whether the pair of equations represents parallel lines, we need to compare the slopes of the two lines.
The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line.
Let's put the given equations in slope-intercept form:
Equation 1: 3x = 5y - 2
Rearrange the equation by isolating y:
5y = 3x + 2
Divide both sides by 5:
y = (3/5)x + 2/5
Equation 2: 10y = 4 - 6x
Rearrange the equation by isolating y:
10y = -6x + 4
Divide both sides by 10:
y = (-6/10)x + 4/10
Simplify the fractions:
y = (-3/5)x + 2/5
Now, compare the slopes of the two equations:
The slope of Equation 1 is 3/5.
The slope of Equation 2 is -3/5.
If two lines have the same slope, they are parallel. Therefore, since the slopes of the two equations are the negative reciprocal of each other, these lines are parallel.