Tell whether the lines for each pair of equation are parallel perpendicular or neither.
y=5/3x+3
20x+12y=12
To determine if two lines are parallel, perpendicular, or neither, we can compare their slopes.
The given equation y = (5/3)x + 3 is in slope-intercept form y = mx + b, where m represents the slope. In this case, the slope of the line is 5/3.
The second equation 20x + 12y = 12 can be rewritten in slope-intercept form by solving for y:
12y = -20x + 12
y = (-20/12)x + 1
y = (-5/3)x + 1
Comparing the slopes of the two equations, we can see that they both have a slope of -5/3. Therefore, the lines are parallel.
To determine whether the lines are parallel, perpendicular, or neither, we can compare the slopes of the two lines.
1) Equation 1: y = (5/3)x + 3
In this equation, the slope (m1) is 5/3.
2) Equation 2: 20x + 12y = 12
To find the slope of this equation, we need to rewrite it in slope-intercept form (y = mx + b):
12y = -20x + 12
y = (-20/12)x + 1
y = (-5/3)x + 1
In this equation, the slope (m2) is -5/3.
Now, let's compare the slopes:
If m1 * m2 = -1, the lines are perpendicular.
If m1 = m2, the lines are parallel.
If neither of the above conditions is met, the lines are neither parallel nor perpendicular.
Now, let's calculate m1 * m2:
(5/3) * (-5/3) = -25/9
Since -25/9 does not equal -1 and m1 does not equal m2, the lines are neither parallel nor perpendicular.
To determine whether the lines represented by these equations are parallel, perpendicular, or neither, we need to compare the slopes of the two lines. The slope-intercept form of a linear equation is in the form y = mx + b, where m represents the slope of the line.
Let's find the slopes of the two lines:
For the first equation, y = (5/3)x + 3, we can identify that the coefficient of x, 5/3, is the slope. So, the slope of the first line is 5/3.
To find the slope of the second equation, we need to rearrange it into the slope-intercept form. The given equation is 20x + 12y = 12. We'll subtract 20x from both sides and then divide the entire equation by 12 to isolate y:
12y = -20x + 12
y = (-20/12)x + 1
y = (-5/3)x + 1
Comparing the slopes of both equations, we can see that the slope of the second line is also -5/3.
Since the slopes of both lines are the same (-5/3), the lines are parallel to each other.