2C Writing 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 is the y-intercept (b) 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 find the slope between two points (x1, y1) and (x2, y2)?

Back

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

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 standard form to slope-intercept form?

Back

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

Front

What is the significance of parallel lines in terms of linear equations?

Back

Parallel lines have the same slope but different y-intercepts. Their equations will have the same m value.

Front

What is the significance of perpendicular lines in terms of linear equations?

Back

Perpendicular lines have slopes that are negative reciprocals of each other. If one line has a slope of m, the other will have a slope of -1/m.

Front

How do you graph a linear equation using the slope and y-intercept?

Back

Start by plotting the y-intercept on the graph. From that point, use the slope to determine the rise over run to plot another point.

Front

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

Back

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