Finding X and Y Intercepts Flashcard

Front

What is the definition of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0.

Front

How do you find the y-intercept of a linear equation in standard form (Ax + By = C)?

Back

To find the y-intercept, set x = 0 and solve for y.

Front

What is the definition of the x-intercept in a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis, which occurs when y = 0.

Front

How do you find the x-intercept of a linear equation in standard form (Ax + By = C)?

Back

To find the x-intercept, set y = 0 and solve for x.

Front

What is the general form of a linear equation?

Back

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

Front

What does the slope of a line represent in a linear equation?

Back

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

Front

How can you determine the slope from two points on a line?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is the relationship between the slope and the y-intercept in the slope-intercept form of a linear equation?

Back

In slope-intercept form (y = mx + b), m represents the slope and b represents the y-intercept.

Front

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

Back

The coefficients A and B determine the slope of the line, while C represents the point where the line intersects the axes.

Front

How can you graph a linear equation using its intercepts?

Back

To graph a linear equation using its intercepts, plot the x-intercept and y-intercept on the coordinate plane and draw a line through these points.