determaine if the two lines are parrallel , perpendicuar, or neither.
line a: y = 4x
line b: x + 4y = 2
To determine if two lines are parallel, perpendicular, or neither, we can compare their slopes. The slope-intercept form of a line is y = mx + b, where m represents the slope.
Let's examine both lines:
Line a: y = 4x
Line b: x + 4y = 2
To find the slope of Line a, we can see that it is in slope-intercept form (y = mx + b) with m = 4. So, the slope of Line a is 4.
To determine the slope of Line b, we need to rearrange its equation into slope-intercept form. Let's isolate y:
x + 4y = 2
4y = -x + 2
y = (-1/4)x + 1/2
Now we can see that the slope of Line b is -1/4.
Comparing the slopes, we have:
Slope of Line a = 4
Slope of Line b = -1/4
Since the slopes are not equal and have different signs, we can conclude that the lines are neither parallel nor perpendicular.