What is the slope of a line that is perpendicular to $$y = \frac{1}{3}x - 9$$ ?

The slope of a line perpendicular to $$y = \frac{1}{3}x - 9$$ is $$-3$$ , which is the negative reciprocal of $$\frac{1}{3}$$ .

What is the solution to the equation $$f(x) = 5x - 25$$ when $$f(x) = 10$$ ?

To find $$x$$ , set $$5x - 25 = 10$$ . Solving gives $$x = 7$$ .

What is the equation of a line parallel to $$y = \frac{3}{2}x - 4$$ ?

Any line with the same slope of $$\frac{3}{2}$$ , such as $$y = \frac{3}{2}x + 1$$ , is parallel.

What is the standard form of a linear equation?

The standard form of a linear equation is $$Ax + By = C$$ , where $$A$$ , $$B$$ , and $$C$$ are integers, and $$A$$ should be non-negative.

What is the graphical representation of a system of inequalities?

The graphical representation consists of shaded regions on a coordinate plane, where each region corresponds to the solutions of each inequality.

How do you find the intersection of two inequalities?

The intersection of two inequalities is found by identifying the region where the shaded areas of both inequalities overlap.

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 as $$(0, b)$$ in the equation $$y = mx + b$$ .

What does it mean for a system of inequalities to be inconsistent?

A system of inequalities is inconsistent if there are no solutions that satisfy all inequalities simultaneously.

How can you graph a system of inequalities?

To graph a system of inequalities, first graph each inequality as if it were an equation, then shade the appropriate region for each inequality.

What is the difference between a solution to an inequality and a solution to an equation?

A solution to an inequality is a range of values that satisfy the inequality, while a solution to an equation is a specific value that makes the equation true.

Systems of Inequalities Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities that share the same variables. The solution is the set of all points that satisfy all inequalities in the system.

Tags

CCSS.8.EE.C.8B

2.

FLASHCARD QUESTION

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.

Tags

CCSS.8.EE.B.5

3.

FLASHCARD QUESTION

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. This means that one line's slope is the negative reciprocal of the other's.

Tags

CCSS.8.EE.B.6

4.

FLASHCARD QUESTION

Front

How do you write an equation in point-slope form?

Back

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.8.EE.B.6

6.

FLASHCARD QUESTION

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is a solution.

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF.IF.A.2

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