How do you convert the equation $$x - 3y = 6$$ to slope-intercept form?

To convert to slope-intercept form, solve for $$y$$ : 1. Rearrange: $$-3y = -x + 6$$ 2. Divide by -3: $$y = \frac{1}{3}x - 2$$ .

Convert the equation $$y - 5 = 7(x - 0)$$ to slope-intercept form.

Distributing gives $$y - 5 = 7x$$ . Adding 5 results in $$y = 7x + 5$$ .

What is the significance of the coefficients in the standard form $$Ax + By = C$$ ?

The coefficients $$A$$ and $$B$$ determine the slope of the line, while $$C$$ represents the y-intercept when $$x = 0$$ .

How can you identify if an equation is in standard form?

An equation is in standard form if it can be expressed as $$Ax + By = C$$ , where $$A$$ , $$B$$ , and $$C$$ are integers and $$A$$ is non-negative.

What is the slope of the line represented by the equation $$7x + 2y = 9$$ ?

To find the slope, rearrange to slope-intercept form: $$2y = -7x + 9$$ , then $$y = -\frac{7}{2}x + \frac{9}{2}$$ . The slope is $$-\frac{7}{2}$$ .

What does the term 'y-intercept' mean?

The y-intercept is the value of $$y$$ when $$x = 0$$ , indicating where the line crosses the y-axis.

How do you find the x-intercept of the equation $$7x + 2y = 9$$ ?

Set $$y = 0$$ and solve for $$x$$ : $$7x = 9$$ , so $$x = \frac{9}{7}$$ .

What is the relationship between slope and parallel lines?

Parallel lines have the same slope but different y-intercepts.

What is the relationship between slope and perpendicular lines?

Perpendicular lines have slopes that are negative reciprocals of each other.

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

Substitute the x and y values of the point into the equation. If the equation holds true, the point lies on the line.

Standard Form 2024 final Flashcards

Student preview

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 is the standard form of a linear equation?

Back

4.

FLASHCARD QUESTION

Front

Identify the y-intercept from the ordered pair (0, 4).

Back

The y-intercept is the point where the line crosses the y-axis, which is represented by the ordered pair (0, 4).

5.

FLASHCARD QUESTION

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x, indicating how steep the line is.

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

Back

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