Writing Linear Equations Given a Point and Slope

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 write the equation of a line given a point (x1, y1) and a slope (m)?

Back

Use the point-slope form: y - y1 = m(x - x1). You can then rearrange it to slope-intercept form (y = mx + b).

Front

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

Back

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

Front

How can you convert point-slope form to slope-intercept form?

Back

To convert, solve for y: y = mx - mx1 + y1, which simplifies to y = mx + b.

Front

What is the significance of a positive slope?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What does a slope of zero mean?

Back

A slope of zero means the line is horizontal, indicating that y does not change as x changes.

Front

What does an undefined slope mean?

Back

An undefined slope means the line is vertical, indicating that x does not change as y changes.