What is the significance of the y-intercept in a linear equation?

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

How can you determine if two lines are intersecting or parallel from their equations?

If the slopes of the two lines are equal, they are parallel. If the slopes are different, they intersect.

What is the general form of a linear equation?

The general form of a linear equation is Ax + By + C = 0, where A, B, and C are constants.

How do you write the equation of a line parallel to a given line?

To write the equation of a line parallel to a given line, use the same slope as the given line and a different y-intercept.

What is the formula for finding the distance between two points in coordinate geometry?

The distance (d) between two points (x1, y1) and (x2, y2) is given by the formula d = √((x2 - x1)² + (y2 - y1)²).

What is the concept of slope in real-world applications?

Slope represents the rate of change, such as speed in a distance-time graph or cost per item in a cost graph.

How can you identify the type of relationship between two lines based on their slopes?

If the slopes are equal, the lines are parallel; if the product of the slopes is -1, the lines are perpendicular; if the slopes are different, the lines intersect.

Coordinate Geometry

Flashcard

•

Mathematics

•

9th - 11th Grade

•

Practice Problem

•

Hard

•

CCSS

8.EE.B.5, HSG.CO.A.1, 8.EE.B.6

Standards-aligned

Wayground Content

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15 questions

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FLASHCARD QUESTION

Front

What is the definition of parallel lines in coordinate geometry?

Back

Parallel lines are lines in a plane that never meet. They have the same slope but different y-intercepts.

Tags

CCSS.4.G.A.1

CCSS.HSG.CO.A.1

FLASHCARD QUESTION

Front

How do you determine if two lines are parallel given their equations?

Back

Two lines are parallel if their slopes are equal. For example, in the equations y = mx + b, if both lines have the same value of m, they are parallel.

FLASHCARD QUESTION

Front

What is the slope of a line represented by the equation y = mx + b?

Back

The slope of the line is represented by the coefficient m in the equation y = mx + b.

Tags

CCSS.8.EE.B.5

FLASHCARD QUESTION

Front

What is the relationship between the slopes of perpendicular lines?

Back

The slopes of perpendicular lines are negative reciprocals of each other. If one line has a slope of m, the other line's slope will be -1/m.

Tags

CCSS.HSG.CO.A.1

FLASHCARD QUESTION

Front

How can you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

FLASHCARD QUESTION

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

FLASHCARD QUESTION

Front

What does it mean for two lines to intersect?

Back

Two lines intersect if they cross each other at a point. This occurs when their slopes are different.

Tags

CCSS.HSG.CO.A.1

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