Forms of Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the slope-intercept form y = mx + b.

Front

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

Back

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

Front

What is point-slope form of a linear equation?

Back

Point-slope form is an equation of a line that passes through a given point (x1, y1) with a slope m, expressed as y - y1 = m(x - x1).

Front

How do you find the slope from two points?

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 does a vertical line represent in a graph?

Back

A vertical line represents an undefined slope and can be described by an equation of the form x = a, where 'a' is a constant.

Front

What does a horizontal line represent in a graph?

Back

A horizontal line has a slope of 0 and can be described by an equation of the form y = b, where 'b' is a constant.

Front

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

Back

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

Front

How do you identify the slope from an equation in slope-intercept form?

Back

In the equation y = mx + b, the slope is the coefficient of x, which is m.