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 'slope' represent in a linear equation?

Back

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

Front

What is the y-intercept in a linear equation?

Back

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

Front

How do you find the slope from 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 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 can you determine if a linear equation is increasing or decreasing?

Back

If the slope (m) is positive, the line is increasing. If the slope is negative, the line is decreasing.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is y = b, where b is the y-value for all points on the line.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is x = a, where a is the x-value for all points on the line.

Front

How do 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, solve for y: y = (-A/B)x + (C/B).

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).