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

The point-slope form of a linear equation is $$y - y_1 = m(x - x_1)$$ , where (x1, y1) is a point on the line and m is the slope.

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

To convert from slope-intercept form $$y = mx + b$$ to standard form $$Ax + By = C$$ , rearrange the equation to isolate the terms involving x and y on one side.

What is the significance of the coefficients in a linear equation?

The coefficients in a linear equation determine the slope and the y-intercept. The coefficient of x (m) indicates the slope, while the constant term (b) indicates the y-intercept.

How can you graph a linear equation?

To graph a linear equation, identify the y-intercept (b) and plot it on the y-axis. Then use the slope (m) to find another point by rising and running from the y-intercept.

What is a system of linear equations?

A system of linear equations is a set of two or more linear equations with the same variables. Solutions to the system are the points where the graphs of the equations intersect.

What does it mean for a system of equations to be consistent?

A system of equations is consistent if it has at least one solution. It can be either independent (one solution) or dependent (infinitely many solutions).

What is the graphical representation of a linear equation?

The graphical representation of a linear equation is a straight line on the Cartesian plane, where each point on the line represents a solution to the equation.

How do you identify the equation of a line from a graph?

To identify the equation of a line from a graph, determine the slope (rise/run) and the y-intercept (where the line crosses the y-axis), then use the slope-intercept form $$y = mx + b$$ .

Linear Equations 12 Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is a linear equation?

Back

2.

FLASHCARD QUESTION

Front

What does the slope of a linear equation represent?

Back

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

3.

FLASHCARD QUESTION

Front

What is the y-intercept in a linear equation?

Back

4.

FLASHCARD QUESTION

Front

How do you find the slope from two points?

Back

5.

FLASHCARD QUESTION

Front

What is the standard form of a linear equation?

Back

6.

FLASHCARD QUESTION

Front

How can you determine if two lines are parallel?

Back

7.

FLASHCARD QUESTION

Front

What does it mean for two lines to be perpendicular?

Back

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