How do you graph the inequality $$y \leq 5x + 4$$ ?

1. Graph the line $$y = 5x + 4$$ as a solid line (since it includes equality). 2. Shade below the line to represent all points where $$y$$ is less than or equal to $$5x + 4$$ .

What does the inequality $$y

It represents all points below the line $$y = \frac{1}{2}x - 4$$ , which is graphed as a dashed line (not including equality).

How do you write the equation of a line parallel to $$y = -x + 5$$ that passes through the point (-5, 2)?

The equation is $$y = -x - 3$$ , using the same slope of -1 and the point-slope form.

What is the point-slope form of a line?

The point-slope form is $$y - y_1 = m(x - x_1)$$ , where $$m$$ is the slope and $$(x_1, y_1)$$ is a point on the line.

What is the difference between a solid line and a dashed line in graphing inequalities?

A solid line indicates that points on the line are included in the solution (e.g., $$y \leq$$ ), while a dashed line indicates they are not included (e.g., $$y

How do you solve for $$y$$ in the equation $$-2x + 8y = 32$$ ?

Rearranging gives $$y = \frac{1}{4}x + 4$$ .

What is the significance of shading in a graph of inequalities?

Shading indicates the region of the graph that satisfies the inequality.

What is an inequality statement?

An inequality statement expresses a relationship between two expressions that are not equal, using symbols like >,

How do you determine which region to shade for a system of inequalities?

Graph each inequality and shade the appropriate region based on whether the inequality is strict or inclusive, then find the overlapping region.

What is the solution set of a system of inequalities?

The solution set is the set of all points that satisfy all inequalities in the system.

Flashcard #6 (2nd Qtr) - ALG 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 with the same variables. The solution is the region where the graphs of the inequalities overlap.

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

How do you find the slope of a line from its equation?

Back

6.

FLASHCARD QUESTION

Front

Back

The slope is -1.

7.

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.

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