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 y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

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 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 then use the formula m = rise/run.

Front

What is the slope of the line represented by the equation y = 1/4x + 2?

Back

The slope of the line is 1/4.

Front

How do you write the equation of a line given the slope and y-intercept?

Back

Use 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 = -3/2x + 4?

Back

The slope of the line is -3/2.

Front

If a line has a slope of 2, what does this mean?

Back

A slope of 2 means that for every 1 unit increase in x, y increases by 2 units.

Front

What is the relationship between the slopes of parallel lines?

Back

Parallel lines have the same slope but different y-intercepts.

Front

What is the relationship between the slopes of perpendicular lines?

Back

Perpendicular lines have slopes that are negative reciprocals of each other (m1 * m2 = -1).