1. tell whether the lines of each pair of equations are parallel or perpendicular or neither
Y=-3x+7
-2x+6y=3
*Perpendicular
2. tell whether the lines of each pair of equations are parallel or perpendicular or neither
Y=-1/4x+10
-2x+8y=6
Neither for second one ^
looks good
To determine whether the lines of each pair of equations are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of a line is given by y = mx + b, where m represents the slope.
Let's start with the first pair of equations:
1. Y = -3x + 7
2. -2x + 6y = 3
To compare the slopes, we need to rewrite the second equation in slope-intercept form. Rearranging equation 2, we get:
-2x + 6y = 3
6y = 2x + 3
y = (2/6)x + (3/6)
y = (1/3)x + 1/2
Now, we can see that equation 1 has a slope of -3, while equation 2 has a slope of 1/3.
Since the slopes are negative reciprocals of each other (-3 and 1/3), the lines represented by these equations are perpendicular to each other.
Now, let's move to the second pair of equations:
1. Y = -(1/4)x + 10
2. -2x + 8y = 6
Again, we need to convert equation 2 into the slope-intercept form:
-2x + 8y = 6
8y = 2x + 6
y = (2/8)x + 6/8
y = (1/4)x + 3/4
Comparing equation 1 and equation 2, we can see that both have a slope of -1/4.
Since the slopes are equal (-1/4 and -1/4), the lines represented by the equations are parallel.
In summary:
1. The lines represented by the equations Y = -3x + 7 and -2x + 6y = 3 are perpendicular.
2. The lines represented by the equations Y = -(1/4)x + 10 and -2x + 8y = 6 are parallel.