QuestionDetermine if the lines $y=\frac{4}{3} x-5$ , $8 x-6 y=6$ , and $3 y=4 x+7$ are parallel, perpendicular, or neither.

Studdy Solution

STEP 1

Assumptions1. The equations of the three lines are given as follows Line1 $y=\frac{4}{3} x-5$ Line $8 x-6 y=6$ Line3 $3 y=4 x+7$
. Two lines are parallel if their slopes are equal.
3. Two lines are perpendicular if the product of their slopes is -1.
4. If neither of these conditions is met, the lines are neither parallel nor perpendicular.

STEP 2

First, we need to find the slopes of the given lines. The slope of a line in the form $y=mx+c$ is $m$ .
The slope of Line1 is $\frac{4}{}$ .

STEP 3

Next, we need to rewrite the equations of Line2 and Line3 in the form $y=mx+c$ to find their slopes.
For Line2, we can rewrite the equation as follows $8x -6y =6 \Rightarrow y = \frac{}{3}x -1$ So, the slope of Line2 is $\frac{}{3}$ .

STEP 4

For Line3, we can rewrite the equation as follows $3y =4x +7 \Rightarrow y = \frac{4}{3}x + \frac{7}{3}$ So, the slope of Line3 is $\frac{4}{3}$ .

STEP 5

Now that we have the slopes of all three lines, we can compare them to determine whether the lines are parallel, perpendicular, or neither.
The slope of Line1 is $\frac{4}{3}$ , the slope of Line2 is $\frac{4}{3}$ , and the slope of Line3 is $\frac{4}{3}$ .

STEP 6

Since all three lines have the same slope, they are all parallel to each other.
Therefore, for each pair of lines, they are parallel.

Was this helpful?

QuestionDetermine if the lines $y=\frac{4}{3} x-5$ , $8 x-6 y=6$ , and $3 y=4 x+7$ are parallel, perpendicular, or neither.

Studdy Solution

STEP 1

STEP 2

First, we need to find the slopes of the given lines. The slope of a line in the form $y=mx+c$ is $m$ .
The slope of Line1 is $\frac{4}{}$ .

STEP 3

Next, we need to rewrite the equations of Line2 and Line3 in the form $y=mx+c$ to find their slopes.
For Line2, we can rewrite the equation as follows $8x -6y =6 \Rightarrow y = \frac{}{3}x -1$ So, the slope of Line2 is $\frac{}{3}$ .

STEP 4

For Line3, we can rewrite the equation as follows $3y =4x +7 \Rightarrow y = \frac{4}{3}x + \frac{7}{3}$ So, the slope of Line3 is $\frac{4}{3}$ .

STEP 5

Now that we have the slopes of all three lines, we can compare them to determine whether the lines are parallel, perpendicular, or neither.
The slope of Line1 is $\frac{4}{3}$ , the slope of Line2 is $\frac{4}{3}$ , and the slope of Line3 is $\frac{4}{3}$ .

STEP 6

Since all three lines have the same slope, they are all parallel to each other.
Therefore, for each pair of lines, they are parallel.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionDetermine if the lines y=43x−5y=\frac{4}{3} x-5y=34​x−5, 8x−6y=68 x-6 y=68x−6y=6, and 3y=4x+73 y=4 x+73y=4x+7 are parallel, perpendicular, or neither.

Studdy Solution

STEP 1

STEP 2

First, we need to find the slopes of the given lines. The slope of a line in the form y=mx+cy=mx+cy=mx+c is mmm.The slope of Line1 is 4\frac{4}{}4​.

STEP 3

Next, we need to rewrite the equations of Line2 and Line3 in the form y=mx+cy=mx+cy=mx+c to find their slopes.For Line2, we can rewrite the equation as follows8x−6y=6⇒y=3x−18x -6y =6 \Rightarrow y = \frac{}{3}x -18x−6y=6⇒y=3​x−1So, the slope of Line2 is 3\frac{}{3}3​.

STEP 4

For Line3, we can rewrite the equation as follows3y=4x+7⇒y=43x+733y =4x +7 \Rightarrow y = \frac{4}{3}x + \frac{7}{3}3y=4x+7⇒y=34​x+37​So, the slope of Line3 is 43\frac{4}{3}34​.

STEP 5

Now that we have the slopes of all three lines, we can compare them to determine whether the lines are parallel, perpendicular, or neither.The slope of Line1 is 43\frac{4}{3}34​, the slope of Line2 is 43\frac{4}{3}34​, and the slope of Line3 is 43\frac{4}{3}34​.

STEP 6

Since all three lines have the same slope, they are all parallel to each other.Therefore, for each pair of lines, they are parallel.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionDetermine if the lines $y=\frac{4}{3} x-5$ , $8 x-6 y=6$ , and $3 y=4 x+7$ are parallel, perpendicular, or neither.

First, we need to find the slopes of the given lines. The slope of a line in the form $y=mx+c$ is $m$ .
The slope of Line1 is $\frac{4}{}$ .

Next, we need to rewrite the equations of Line2 and Line3 in the form $y=mx+c$ to find their slopes.
For Line2, we can rewrite the equation as follows $8x -6y =6 \Rightarrow y = \frac{}{3}x -1$ So, the slope of Line2 is $\frac{}{3}$ .

For Line3, we can rewrite the equation as follows $3y =4x +7 \Rightarrow y = \frac{4}{3}x + \frac{7}{3}$ So, the slope of Line3 is $\frac{4}{3}$ .

Now that we have the slopes of all three lines, we can compare them to determine whether the lines are parallel, perpendicular, or neither.
The slope of Line1 is $\frac{4}{3}$ , the slope of Line2 is $\frac{4}{3}$ , and the slope of Line3 is $\frac{4}{3}$ .

Since all three lines have the same slope, they are all parallel to each other.
Therefore, for each pair of lines, they are parallel.