3 Linear Forms

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 should be non-negative.

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

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

Back

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

Front

Convert the equation 3x + 4y = 12 to slope-intercept form.

Back

y = -3/4x + 3.

Front

Convert the equation y = 2x + 5 to standard form.

Back

2x - y = -5.

Front

Identify the slope in the equation y = -1/2x + 4.

Back

The slope is -1/2.

Front

Identify the y-intercept in the equation y = 5x - 3.

Back

The y-intercept is -3.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What does the y-intercept of a line represent?

Back

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

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope m is calculated as m = (y2 - y1) / (x2 - x1).