Question Find the slopes of parallel and perpendicular lines given by $y=\frac{1}{2}x+7$ and $y=-2x-3$ . Compare the slopes to determine their relationship.

Studdy Solution

STEP 1

Assumptions
1. The slope of a line parallel to another is equal to the slope of that line.
2. The slope of a line perpendicular to another is the negative reciprocal of the slope of that line.
3. The equations of the lines are given in slope-intercept form, $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 2

Identify the slope of the line given in Column A.
The equation of the line in Column A is in the form $y = mx + b$ , where $m$ is the slope. For the line $y = \frac{1}{2}x + 7$ , the slope $m$ is $\frac{1}{2}$ .

STEP 3

Since a line parallel to another line has the same slope, the slope of the line in Column A is $\frac{1}{2}$ .

STEP 4

Identify the slope of the line given in Column B.
The equation of the line in Column B is also in the form $y = mx + b$ . For the line $y = -2x - 3$ , the slope $m$ is $-2$ .

STEP 5

Find the slope of a line perpendicular to the line given in Column B.
To find the slope of a line perpendicular to another, we take the negative reciprocal of the slope of the original line. The negative reciprocal of $-2$ is $\frac{1}{2}$ .

STEP 6

Compare the slopes identified in Column A and Column B.
The slope of the line in Column A is $\frac{1}{2}$ , and the slope of a line perpendicular to the line in Column B is also $\frac{1}{2}$ .

STEP 7

Since both slopes are equal, the quantity in Column A is equal to the quantity in Column B.
The correct answer is C. The two quantities are equal.

Was this helpful?

Question Find the slopes of parallel and perpendicular lines given by $y=\frac{1}{2}x+7$ and $y=-2x-3$ . Compare the slopes to determine their relationship.

Studdy Solution

STEP 1

STEP 2

Identify the slope of the line given in Column A.
The equation of the line in Column A is in the form $y = mx + b$ , where $m$ is the slope. For the line $y = \frac{1}{2}x + 7$ , the slope $m$ is $\frac{1}{2}$ .

STEP 3

Since a line parallel to another line has the same slope, the slope of the line in Column A is $\frac{1}{2}$ .

STEP 4

Identify the slope of the line given in Column B.
The equation of the line in Column B is also in the form $y = mx + b$ . For the line $y = -2x - 3$ , the slope $m$ is $-2$ .

STEP 5

Find the slope of a line perpendicular to the line given in Column B.
To find the slope of a line perpendicular to another, we take the negative reciprocal of the slope of the original line. The negative reciprocal of $-2$ is $\frac{1}{2}$ .

STEP 6

Compare the slopes identified in Column A and Column B.
The slope of the line in Column A is $\frac{1}{2}$ , and the slope of a line perpendicular to the line in Column B is also $\frac{1}{2}$ .

STEP 7

Since both slopes are equal, the quantity in Column A is equal to the quantity in Column B.
The correct answer is C. The two quantities are equal.

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.

Question Find the slopes of parallel and perpendicular lines given by y=12x+7y=\frac{1}{2}x+7y=21​x+7 and y=−2x−3y=-2x-3y=−2x−3. Compare the slopes to determine their relationship.

Studdy Solution

STEP 1

STEP 2

Identify the slope of the line given in Column A.The equation of the line in Column A is in the form y=mx+by = mx + by=mx+b, where mmm is the slope. For the line y=12x+7y = \frac{1}{2}x + 7y=21​x+7, the slope mmm is 12\frac{1}{2}21​.

STEP 3

Since a line parallel to another line has the same slope, the slope of the line in Column A is 12\frac{1}{2}21​.

STEP 4

Identify the slope of the line given in Column B.The equation of the line in Column B is also in the form y=mx+by = mx + by=mx+b. For the line y=−2x−3y = -2x - 3y=−2x−3, the slope mmm is −2-2−2.

STEP 5

Find the slope of a line perpendicular to the line given in Column B.To find the slope of a line perpendicular to another, we take the negative reciprocal of the slope of the original line. The negative reciprocal of −2-2−2 is 12\frac{1}{2}21​.

STEP 6

Compare the slopes identified in Column A and Column B.The slope of the line in Column A is 12\frac{1}{2}21​, and the slope of a line perpendicular to the line in Column B is also 12\frac{1}{2}21​.

STEP 7

Since both slopes are equal, the quantity in Column A is equal to the quantity in Column B.The correct answer is C. The two quantities are equal.

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.

Question Find the slopes of parallel and perpendicular lines given by $y=\frac{1}{2}x+7$ and $y=-2x-3$ . Compare the slopes to determine their relationship.

Identify the slope of the line given in Column A.
The equation of the line in Column A is in the form $y = mx + b$ , where $m$ is the slope. For the line $y = \frac{1}{2}x + 7$ , the slope $m$ is $\frac{1}{2}$ .

Since a line parallel to another line has the same slope, the slope of the line in Column A is $\frac{1}{2}$ .

Identify the slope of the line given in Column B.
The equation of the line in Column B is also in the form $y = mx + b$ . For the line $y = -2x - 3$ , the slope $m$ is $-2$ .

Find the slope of a line perpendicular to the line given in Column B.
To find the slope of a line perpendicular to another, we take the negative reciprocal of the slope of the original line. The negative reciprocal of $-2$ is $\frac{1}{2}$ .

Compare the slopes identified in Column A and Column B.
The slope of the line in Column A is $\frac{1}{2}$ , and the slope of a line perpendicular to the line in Column B is also $\frac{1}{2}$ .

Since both slopes are equal, the quantity in Column A is equal to the quantity in Column B.
The correct answer is C. The two quantities are equal.