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![Determine whether the lines are parallel, perpendicular or neither.
{:[y=(3)/(4)x+2],[8x+6y=12]:}
Parallel](https://blblobstorage.blob.core.windows.net/solver-b2c/d66b705e-f74d-11ee-bf16-92c5a7e9433c.jpg)
Determine whether the lines are parallel, perpendicular or neither.Parallel perpendicular neither
Full solution
Q. Determine whether the lines are parallel, perpendicular or neither.Parallel perpendicular neither
- Find Slope First Line: To determine the relationship between the two lines, we need to find their slopes. If the slopes are equal, the lines are parallel. If the product of the slopes is , the lines are perpendicular. Otherwise, they are neither parallel nor perpendicular.
- Find Slope Second Line: First, let's find the slope of the first line given by . The slope-intercept form of a line is , where is the slope. Here, the slope is clearly .
- Determine Relationship: Now, let's find the slope of the second line given by . We need to rearrange this equation into slope-intercept form, . Let's solve for .
- Isolate y Term: Subtract from both sides of the equation to isolate the term on one side:
- Solve for y: Now, divide both sides of the equation by to solve for y:
- Simplify Fractions: Simplify the fractions:The slope of the second line is .
- Check Parallel Lines: Now we have the slopes of both lines: the first line has a slope of , and the second line has a slope of . Since these slopes are not equal, the lines are not parallel. To check if they are perpendicular, we multiply the slopes and see if the product is .
- Calculate Slope Product: Multiply the slopes :(\frac{\(3\)}{\(4\)}) \times (-\frac{\(4\)}{\(3\)}) = \(-1
- Lines are Perpendicular: The product of the slopes is , which means the lines are perpendicular to each other.
