Determine whether the lines are parallel, perpendicular or neither. {:[y=(3)/(4)x+2],[8x+6y=12]:} Parallel

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Determine whether the lines are parallel, perpendicular or neither.  {:[y=(3)/(4)x+2],[8x+6y=12]:} Parallel

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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 -1, 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 y=(3/4)x+2. The slope-intercept form of a line is y=mx+b, where m is the slope. Here, the slope m is clearly (3/4).Determine Relationship: Now, let's find the slope of the second line given by 8x+6y=12. We need to rearrange this equation into slope-intercept form, y=mx+b. Let's solve for y.Isolate y Term: Subtract 8x from both sides of the equation 8x+6y=12 to isolate the y term on one side: 6y = -8x + 12Solve for y: Now, divide both sides of the equation by 6 to solve for y: y = (-8/6)x + (12/6)Simplify Fractions: Simplify the fractions: y = (-4/3)x + 2 The slope of the second line is -4/3.Check Parallel Lines: Now we have the slopes of both lines: the first line has a slope of 3/4, and the second line has a slope of -4/3. 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 -1.Calculate Slope Product: Multiply the slopes (3/4) * (-4/3): (3/4) * (-4/3) = -1Lines are Perpendicular: The product of the slopes is -1, which means the lines are perpendicular to each other.

Determine whether the lines are parallel, perpendicular or neither. $\newline$ $\begin{array}{l} y=\frac{3}{4} x+2 \\ 8 x+6 y=12 \end{array}$ $\newline$ Parallel $\newline$ perpendicular $\newline$ neither

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Determine whether the lines are parallel, perpendicular or neither.\newliney=34x+28x+6y=12 \begin{array}{l} y=\frac{3}{4} x+2 \\ 8 x+6 y=12 \end{array} y=43​x+28x+6y=12​\newlineParallel \newlineperpendicular \newlineneither

Determine whether the lines are parallel, perpendicular or neither. $\newline$ $\begin{array}{l} y=\frac{3}{4} x+2 \\ 8 x+6 y=12 \end{array}$ $\newline$ Parallel $\newline$ perpendicular $\newline$ neither