Determine wheter the graphs of the given equations are parallel, perpendicular, or neither
y=4x-2
-x+4y=0
neither
y=4x-2 slope 4
y=x/4 slope 1/4
not parallel (same slope)
not perpendicular (negative reciprocal slopes)
To determine whether the graphs of the given equations are parallel, perpendicular, or neither, we need to compare their slopes.
The given equations are:
1. y = 4x - 2
2. -x + 4y = 0
To compare slopes, we need to rewrite the second equation in slope-intercept form, y = mx + b.
Let's solve the second equation for y:
-x + 4y = 0
4y = x
y = (1/4)x
Now we can compare the slopes by looking at the coefficients of x in both equations:
The coefficient of x in the first equation is 4.
The coefficient of x in the second equation is 1/4.
Since the slopes are not equal (4 vs. 1/4), the graphs of the given equations are neither parallel nor perpendicular.
To determine whether the graphs of the given equations are parallel, perpendicular, or neither, we need to compare their slopes. The slope-intercept form of an equation is y = mx + b, where m is the slope.
Given the equations:
1. y = 4x - 2
2. -x + 4y = 0
Let's first rewrite the second equation in slope-intercept form:
-x + 4y = 0
4y = x
y = (1/4)x
Now we can compare the slopes. The slope of the first equation is 4, while the slope of the second equation is 1/4.
Since the slopes are not equal (4 ≠ 1/4), the graphs are not parallel.
To determine if the graphs are perpendicular, we can check if the product of their slopes is -1. However, the product of 4 and 1/4 is 1, not -1. Therefore, the graphs are neither parallel nor perpendicular.
Hence, the graphs of the given equations are neither parallel nor perpendicular.