Question

In the following exercise, use slopes and y-intercepts to determine if the lines are parallel, perpendicular, or neither.

$8x+6y=6$;$12x+9y=12$

Short answer

The given lines are parallel.

Step-by-step solution

Step 1. Given information 

The given equations are$8x+6y=6$and$12x+9y=12$.

Step 2. Solve for y.

Solve both the equations to obtain the value of $y$in terms of $x$.

$\begin{array}{rcl}8x+6y& =& 6\\ 6y& =& 6-8x\\ \frac{6y}{6}& =& \frac{6-8x}{6}\\ y& =& 1-\frac{4}{3}x\end{array}$

$\begin{array}{rcl}12x+9y& =& 12\\ 9y& =& 12-12x\\ \frac{9y}{9}& =& \frac{12-12x}{9}\\ y& =& \frac{4}{3}-\frac{4}{3}x\end{array}$

Step 3. Determine slope and y- intercepts.

• Now both equations are in slope-intercept form.
• Determine the slope by comparing both equations with $y=mx+b$.

$m=-\frac{4}{3}$

• The y-intercept of first and second line is $\left(0,1\right)$and$\left(0,\frac{4}{3}\right)$respectively.

Step 4. Conclusion

Since both the lines have same slope but distinct values of y-intercepts, they are parallel.