Are these equations parallel perpendicular or neither?
Step 1. Need to put above equation given in standard form to slope-intercept form y=mx+b where m is the slope and b is the y-intecept at x=0 or at point (0,b). Two lines are parallel when the slopes are equal while two lines are perpendicular when the product of their slopes is equal to 1.
Step 2. Let's put in slope-intercept form to find the slope.
Subtract 4x from both sides of the equation
Divide 2 to both sides of equation
where the slope m=-2 and the y-intercept b=3/2
Step 3. Now, let's put in slope-intercept form.
Add 4y-6 to both sides of the equation
}
Divide by 4 to both sides of the equation
where the slope m=1/2 and y-intercept b=-3/2}}}
Step 4. ANSWER: Since the product of the slopes found in Steps 2 and 3 is equal to -1, that is, the lines are PERPENDICULAR.
Here's a graph of the above problem. Note the slopes and the y-intercepts at x=0.
I hope the above steps were helpful.
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