Question Describe the coordinate graph of two distinct parallel lines: $\square \quad$ same slopes and different intercepts, $\square \quad$ different slopes and different intercepts.

Studdy Solution

STEP 1

Assumptions
1. We are considering the properties of two distinct parallel lines.
2. The properties in question are related to the slopes and intercepts of the lines.
3. The coordinate graph is a standard Cartesian plane.

STEP 2

Recall the definition of parallel lines in a coordinate plane.
Parallel lines are lines in a plane that do not intersect or meet each other at any point, no matter how far they are extended.

STEP 3

Recall the slope-intercept form of a line.
The slope-intercept form of a line is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 4

Understand the role of the slope in the graph of a line.
The slope ( $m$ ) determines the steepness or the angle of the line with respect to the x-axis. For two lines to be parallel, they must have the same steepness or angle.

STEP 5

Understand the role of the y-intercept in the graph of a line.
The y-intercept ( $b$ ) is the point where the line crosses the y-axis. It is the value of $y$ when $x = 0$ .

STEP 6

Analyze the first option: same slopes and same intercepts.
If two lines have the same slope and the same y-intercept, they would not be distinct; they would be the same line because they would overlap completely.

STEP 7

Analyze the second option: same slopes and different intercepts.
If two lines have the same slope but different y-intercepts, they will never intersect because they rise at the same rate but start from different points on the y-axis. This is the definition of parallel lines.

STEP 8

Analyze the third option: different slopes and same intercepts.
If two lines have different slopes but the same y-intercept, they will intersect at the y-axis and then diverge from each other, so they are not parallel.

STEP 9

Analyze the fourth option: different slopes and different intercepts.
If two lines have different slopes and different y-intercepts, they will intersect at some point unless one is vertical and the other is horizontal. However, in general, they are not parallel.

STEP 10

Conclude which properties describe the coordinate graph of two distinct parallel lines.
The correct properties for two distinct parallel lines are "same slopes and different intercepts" because this ensures that the lines are parallel (same slope) and distinct (different intercepts).
The solution to the problem is: same slopes and different intercepts.

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Question Describe the coordinate graph of two distinct parallel lines: $\square \quad$ same slopes and different intercepts, $\square \quad$ different slopes and different intercepts.

Studdy Solution

STEP 1

Assumptions
1. We are considering the properties of two distinct parallel lines.
2. The properties in question are related to the slopes and intercepts of the lines.
3. The coordinate graph is a standard Cartesian plane.

STEP 2

Recall the definition of parallel lines in a coordinate plane.
Parallel lines are lines in a plane that do not intersect or meet each other at any point, no matter how far they are extended.

STEP 3

Recall the slope-intercept form of a line.
The slope-intercept form of a line is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

STEP 4

Understand the role of the slope in the graph of a line.
The slope ( $m$ ) determines the steepness or the angle of the line with respect to the x-axis. For two lines to be parallel, they must have the same steepness or angle.

STEP 5

Understand the role of the y-intercept in the graph of a line.
The y-intercept ( $b$ ) is the point where the line crosses the y-axis. It is the value of $y$ when $x = 0$ .

STEP 6

Analyze the first option: same slopes and same intercepts.
If two lines have the same slope and the same y-intercept, they would not be distinct; they would be the same line because they would overlap completely.

STEP 7

Analyze the second option: same slopes and different intercepts.
If two lines have the same slope but different y-intercepts, they will never intersect because they rise at the same rate but start from different points on the y-axis. This is the definition of parallel lines.

STEP 8

Analyze the third option: different slopes and same intercepts.
If two lines have different slopes but the same y-intercept, they will intersect at the y-axis and then diverge from each other, so they are not parallel.

STEP 9

Analyze the fourth option: different slopes and different intercepts.
If two lines have different slopes and different y-intercepts, they will intersect at some point unless one is vertical and the other is horizontal. However, in general, they are not parallel.

STEP 10

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Question Describe the coordinate graph of two distinct parallel lines: □\square \quad□ same slopes and different intercepts, □\square \quad□ different slopes and different intercepts.

Studdy Solution

STEP 1

Assumptions1. We are considering the properties of two distinct parallel lines.2. The properties in question are related to the slopes and intercepts of the lines.3. The coordinate graph is a standard Cartesian plane.

STEP 2

Recall the definition of parallel lines in a coordinate plane.Parallel lines are lines in a plane that do not intersect or meet each other at any point, no matter how far they are extended.

STEP 3

Recall the slope-intercept form of a line.The slope-intercept form of a line is given by y=mx+by = mx + by=mx+b, where mmm is the slope and bbb is the y-intercept.

STEP 4

Understand the role of the slope in the graph of a line.The slope (mmm) determines the steepness or the angle of the line with respect to the x-axis. For two lines to be parallel, they must have the same steepness or angle.

STEP 5

Understand the role of the y-intercept in the graph of a line.The y-intercept (bbb) is the point where the line crosses the y-axis. It is the value of yyy when x=0x = 0x=0.

STEP 6

Analyze the first option: same slopes and same intercepts.If two lines have the same slope and the same y-intercept, they would not be distinct; they would be the same line because they would overlap completely.

STEP 7

Analyze the second option: same slopes and different intercepts.If two lines have the same slope but different y-intercepts, they will never intersect because they rise at the same rate but start from different points on the y-axis. This is the definition of parallel lines.

STEP 8

Analyze the third option: different slopes and same intercepts.If two lines have different slopes but the same y-intercept, they will intersect at the y-axis and then diverge from each other, so they are not parallel.

STEP 9

Analyze the fourth option: different slopes and different intercepts.If two lines have different slopes and different y-intercepts, they will intersect at some point unless one is vertical and the other is horizontal. However, in general, they are not parallel.

STEP 10

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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 Describe the coordinate graph of two distinct parallel lines: $\square \quad$ same slopes and different intercepts, $\square \quad$ different slopes and different intercepts.

Assumptions
1. We are considering the properties of two distinct parallel lines.
2. The properties in question are related to the slopes and intercepts of the lines.
3. The coordinate graph is a standard Cartesian plane.

Recall the definition of parallel lines in a coordinate plane.
Parallel lines are lines in a plane that do not intersect or meet each other at any point, no matter how far they are extended.

Recall the slope-intercept form of a line.
The slope-intercept form of a line is given by $y = mx + b$ , where $m$ is the slope and $b$ is the y-intercept.

Understand the role of the slope in the graph of a line.
The slope ( $m$ ) determines the steepness or the angle of the line with respect to the x-axis. For two lines to be parallel, they must have the same steepness or angle.

Understand the role of the y-intercept in the graph of a line.
The y-intercept ( $b$ ) is the point where the line crosses the y-axis. It is the value of $y$ when $x = 0$ .

Analyze the first option: same slopes and same intercepts.
If two lines have the same slope and the same y-intercept, they would not be distinct; they would be the same line because they would overlap completely.

Analyze the second option: same slopes and different intercepts.
If two lines have the same slope but different y-intercepts, they will never intersect because they rise at the same rate but start from different points on the y-axis. This is the definition of parallel lines.

Analyze the third option: different slopes and same intercepts.
If two lines have different slopes but the same y-intercept, they will intersect at the y-axis and then diverge from each other, so they are not parallel.

Analyze the fourth option: different slopes and different intercepts.
If two lines have different slopes and different y-intercepts, they will intersect at some point unless one is vertical and the other is horizontal. However, in general, they are not parallel.