Writing Linear Equations from Graphs

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 y-value with respect to the x-value. It indicates how steep the line is and the direction it goes.

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, calculate the rise (change in y) and run (change in x), and use the formula m = rise/run.

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 can you write the equation of a line given its slope and y-intercept?

Back

You can write the equation using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of the line represented by the equation y = -3x - 3?

Back

The slope of the line is -3.

Front

What is the equation of a horizontal line?

Back

The equation of a horizontal line is of the form y = c, where c is a constant.

Front

What is the equation of a vertical line?

Back

The equation of a vertical line is of the form x = c, where c is a constant.

Front

How do you determine if a line is increasing or decreasing?

Back

A line is increasing if the slope is positive (rises from left to right) and decreasing if the slope is negative (falls from left to right).

Front

What does it mean if a line has a slope of 0?

Back

A line with a slope of 0 is horizontal, meaning there is no change in y as x changes.