How do you determine if two lines are parallel?

Two lines are parallel if they have the same slope.

How do you determine if two lines are perpendicular?

Two lines are perpendicular if the product of their slopes is -1.

What is the slope of the line that passes through the points (1, 3) and (4, 8)?

The slope is $$\frac{8 - 3}{4 - 1} = \frac{5}{3}$$ .

What is the equation of a line with a slope of -2 that passes through the point (1, 1)?

The equation is $$y - 1 = -2(x - 1)$$ , which simplifies to $$y = -2x + 3$$ .

What does the term 'slope' represent in a linear function?

The slope represents the rate of change of y with respect to x.

Comparisons: Linear Functions Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the slope of a horizontal line?

Back

0

2.

FLASHCARD QUESTION

Front

What is the slope of a vertical line?

Back

Undefined

3.

FLASHCARD QUESTION

Front

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

Back

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

4.

FLASHCARD QUESTION

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope $m$ is calculated as $m = \frac{y2 - y1}{x2 - x1}$ .

5.

FLASHCARD QUESTION

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that the line rises as it moves from left to right.

6.

FLASHCARD QUESTION

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that the line falls as it moves from left to right.

7.

FLASHCARD QUESTION

Front

What is the y-intercept of the line represented by the equation $y = -\frac{3}{4}x + 2$ ?

Back

The y-intercept is 2.

8.

FLASHCARD QUESTION

Front

How do you convert the point-slope form of a line to slope-intercept form?

Back

Start with $y - y1 = m(x - x1)$ and solve for $y$ to get it in the form $y = mx + b$ .

9.

FLASHCARD QUESTION

Front

What is the equation of a line with a slope of $\frac{2}{3}$ that passes through the point (0, 0)?

Back

The equation is $y = \frac{2}{3}x$ .

10.

FLASHCARD QUESTION

Front

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

Back

The graph is a straight line that crosses the y-axis at 2 and has a slope of -1.

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