What does the point (x_1, y_1) represent in the point-slope form?

The point (x_1, y_1) represents a specific point on the line.

What is the significance of the slope in the equation $$y + 1 = -2(x - 1)$$ ?

The slope is -2, indicating that for every 1 unit increase in x, y decreases by 2 units.

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

Substitute the x-value of the point into the equation and check if the resulting y-value matches the y-value of the point.

What is the general form of a linear equation?

The general form of a linear equation is $$Ax + By + C = 0$$ , where A, B, and C are constants.

What is the relationship between point-slope form and slope-intercept form?

Point-slope form can be converted to slope-intercept form by solving for y, which provides the slope and y-intercept directly.

How can you find the slope from two points (x_1, y_1) and (x_2, y_2)?

The slope (m) can be calculated using the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ .

Point-Slope Form Flashcards: 15 Cards (9th Grade)

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15 questions

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1.

FLASHCARD QUESTION

Front

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

Back

The point-slope form of a linear equation is given by: $y - y_1 = m(x - x_1)$ , where (x_1, y_1) is a point on the line and m is the slope.

2.

FLASHCARD QUESTION

Front

How do you convert from point-slope form to slope-intercept form?

Back

To convert from point-slope form $y - y_1 = m(x - x_1)$ to slope-intercept form, solve for y: $y = mx - mx_1 + y_1$ .

3.

FLASHCARD QUESTION

Front

What does the slope (m) represent in a linear equation?

Back

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

4.

FLASHCARD QUESTION

Front

What is the slope of the line represented by the equation $y - 2 = 9(x + 1)$ ?

Back

The slope of the line is 9.

5.

FLASHCARD QUESTION

Front

Convert the equation $y - 2 = 9(x + 1)$ into slope-intercept form.

Back

The slope-intercept form is $y = 9x + 11$ .

6.

FLASHCARD QUESTION

Front

What is the y-intercept of the line $y + 5 = -3(x - 6)$ ?

Back

The y-intercept is 13.

7.

FLASHCARD QUESTION

Front

Convert the equation $y + 5 = -3(x - 6)$ into slope-intercept form.

Back

The slope-intercept form is $y = -3x + 13$ .

9.

FLASHCARD QUESTION

Front

Identify the slope and point from the equation $y - 3 = 2(x + 4)$ .

Back

The slope is 2 and the point is (-4, 3).

10.

FLASHCARD QUESTION

Front

Write the equation in point-slope form of the line that passes through the point (4, -7) and has a slope of -1/4.

Back

The equation is $y + 7 = -\frac{1}{4}(x - 4)$ .

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