Graphing Linear Equations

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 of a line represent?

Back

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

Front

What is the y-intercept of a graph?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented as (0, b) in the equation y = mx + b.

Front

How do you find the y-intercept from an equation?

Back

To find the y-intercept from an equation in the form y = mx + b, set x = 0 and solve for y. The value of y will be the y-intercept.

Front

What is the x-intercept of a graph?

Back

The x-intercept is the point where the line crosses the x-axis. It is represented as (a, 0) in the equation.

Front

How do you find the x-intercept from an equation?

Back

To find the x-intercept from an equation in the form y = mx + b, set y = 0 and solve for x. The value of x will be the x-intercept.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope but different y-intercepts. They will 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. This means one line rises while the other falls.

Front

How do you write the equation of a line given a slope and a point?

Back

Use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

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

Back

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