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 rearrange it to slope-intercept form (y = mx + b) if needed.

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 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). They never intersect.

Front

What does it mean for two lines to be perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1. If one slope is m, the other slope is -1/m.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

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

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates in various contexts.