Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$For the given pair of equations, give the slopes of the lines, and then determine whether the two lines are parallel, perpendicular, or neither. {:[12 x-12 y=3],[12 x+16 y=-9]:} Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of 12 x-12 y=3 is ◻ . (Type an integer or a simplified fraction.) B. The slope of 12 x-12 y=3 is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The slope of 12 x+16 y=-9 is ◻ . (Type an integer or a simplified fraction.) B. The slope of 12 x+16 y=-9 is undefined. The lines are ◻$

For the given pair of equations, give the slopes of the lines, and then determine whether the two lines are parallel, perpendicular, or neither. $\newline$ $\begin{array}{l} 12 x-12 y=3 \\ 12 x+16 y=-9 \end{array}$ $\newline$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. $\newline$ A. The slope of $12 x-12 y=3$ is $\square$ . $\newline$ (Type an integer or a simplified fraction.) $\newline$ B. The slope of $12 x-12 y=3$ is undefined. $\newline$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. $\newline$ A. The slope of $12 x+16 y=-9$ is $\square$ . $\newline$ (Type an integer or a simplified fraction.) $\newline$ B. The slope of $12 x+16 y=-9$ is undefined. $\newline$ The lines are $\square$

View step-by-step help

Home

Math Problems

Algebra 2

Solve trigonometric equations I

Full solution

Q. For the given pair of equations, give the slopes of the lines, and then determine whether the two lines are parallel, perpendicular, or neither.

\newline

\begin{array}{l} 12 x-12 y=3 \\ 12 x+16 y=-9 \end{array}

\newline

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

\newline

A. The slope of

12 x-12 y=3

\square

\newline

(Type an integer or a simplified fraction.)

\newline

B. The slope of

12 x-12 y=3

is undefined.

\newline

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

\newline

A. The slope of

12 x+16 y=-9

\square

\newline

(Type an integer or a simplified fraction.)

\newline

B. The slope of

12 x+16 y=-9

is undefined.

\newline

The lines are

\square

Isolate $y$ by adding and subtracting: To isolate $y$ , we add $12y$ to both sides and then subtract $3$ from both sides: $12x = 12y + 3$ .
Divide by $12$ to solve: Now, divide everything by $12$ to solve for $y$ : $y = x - \frac{1}{4}$ .
Find slope of first line: The slope of the first line is the coefficient of $x$ , which is $1$ .
Rewrite second line in slope-intercept form: Now, let's find the slope of the second line $12x + 16y = -9$ by rewriting it in slope-intercept form.
Divide by $16$ to solve for $y$ : Subtract $12x$ from both sides to get $16y = -12x - 9$ .
Compare slopes of the lines: Divide everything by $16$ to solve for $y$ : $y = -\frac{3}{4}x - \frac{9}{16}.$
Conclusion about line relationship: The slope of the second line is the coefficient of $x$ , which is $-\frac{3}{4}$ .
Conclusion about line relationship: The slope of the second line is the coefficient of $x$ , which is $-\frac{3}{4}$ .Now we compare the slopes: the first line has a slope of $1$ , and the second line has a slope of $-\frac{3}{4}$ .
Conclusion about line relationship: The slope of the second line is the coefficient of $x$ , which is $-\frac{3}{4}$ .Now we compare the slopes: the first line has a slope of $1$ , and the second line has a slope of $-\frac{3}{4}$ .Since the slopes are not equal and not negative reciprocals of each other, the lines are neither parallel nor perpendicular.