How do you convert the equation $$2x + 4y = 8$$ into slope-intercept form?

To convert to slope-intercept form, subtract $$2x$$ from both sides to isolate $$y$$ : $$4y = -2x + 8$$ , then divide by 4: $$y = -\frac{1}{2}x + 2$$ .

What is the y-intercept of the equation $$y = 2x + 3$$ ?

The y-intercept is the point where the line crosses the y-axis, which is $$3$$ in this case.

How do you find the x-intercept of the equation $$y = 2x + 3$$ ?

To find the x-intercept, set $$y = 0$$ and solve for $$x$$ : $$0 = 2x + 3$$ , leading to $$x = -\frac{3}{2}$$ .

What is the standard form of a linear equation?

The standard form is given by $$Ax + By = C$$ , where $$A$$ , $$B$$ , and $$C$$ are integers.

What is the first step to solve the equation $$y = mx + b$$ for $$x$$ ?

The first step is to subtract $$b$$ from both sides: $$y - b = mx$$ .

What does the term 'rate of change' refer to in linear equations?

The rate of change refers to the slope of the line, indicating how much $$y$$ changes for a unit change in $$x$$ .

What is the solution set of an inequality?

The solution set of an inequality is the set of all values that satisfy the inequality.

How do you determine if a point lies on the line represented by an equation?

To determine if a point lies on the line, substitute the x and y values of the point into the equation. If the equation holds true, the point lies on the line.

What is the significance of the coefficients in the equation $$y = mx + b$$ ?

The coefficient $$m$$ represents the slope, while $$b$$ represents the y-intercept, indicating where the line crosses the y-axis.

What is the graphical representation of the inequality @@y eq 3x - 5@@?

The graphical representation is a dashed line for the equation $$y = 3x - 5$$ , with shading on one side to indicate the region that satisfies the inequality.

U2 Equations and Inequalities Review Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the slope-intercept form of a linear equation?

Back

2.

FLASHCARD QUESTION

Front

Back

3.

FLASHCARD QUESTION

Front

What does the slope of a line represent?

Back

4.

FLASHCARD QUESTION

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing that one is greater than, less than, or not equal to the other.

5.

FLASHCARD QUESTION

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding equation as a line, then shade the region that satisfies the inequality.

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

Back

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