Writing Linear Equations from Graph

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 (m) represent in a linear equation?

Back

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

Front

What is the y-intercept in 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 equation y = mx + b.

Front

How do you find the slope from two points on a graph?

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 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

How can you convert a linear equation 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 and the constant on the other.

Front

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

Back

The x-intercept is the point where the line crosses the x-axis. It can be found by setting y = 0 in the equation and solving for x.

Front

How do you graph a linear equation?

Back

To graph a linear equation, identify the y-intercept, plot it on the graph, and use the slope to find another point. Draw a straight line through the points.

Front

What does it mean if two linear equations are parallel?

Back

Two linear equations are parallel if they have the same slope (m) but different y-intercepts (b). They will never intersect.

Front

What does it mean if two linear equations are perpendicular?

Back

Two linear equations are perpendicular if the product of their slopes is -1. This means that one slope is the negative reciprocal of the other.