Writing & Graphing 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 (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 does the y-intercept (b) represent in a linear equation?

Back

The y-intercept (b) is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

How do you graph a linear equation?

Back

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

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = k, where k is a constant. This means that y remains the same for all values of x.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = h, where h is a constant. This means that x remains the same for all values of y.

Front

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

Back

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

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 does it mean if two lines are parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts. They never intersect.

Front

What does it mean if two lines are perpendicular?

Back

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