Writing Linear Equations: Standard Form

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A and B are not both zero.

Front

How do you find the x-intercept of a linear equation?

Back

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

Front

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

Back

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented as (0, b) in the slope-intercept form.

Front

How can you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y.

Front

What is the significance of the coefficients A, B, and C in the standard form of a linear equation?

Back

A represents the coefficient of x, B represents the coefficient of y, and C is the constant term. They determine the line's position and slope.

Front

What is the graphical representation of the equation x = -2?

Back

The equation x = -2 represents a vertical line that crosses the x-axis at -2.

Front

How do you determine if a point (x, y) lies on the line represented by a linear equation?

Back

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

Front

What is the relationship between the slope of a line and its steepness?

Back

The slope of a line indicates its steepness; a larger absolute value of the slope means a steeper line.